PB161 Programming in C++ 1/114 June 28, 2022
PB161 Programming in C++
Petr Ročkai
Part A: Preliminaries
This document is a collection of exercises and commented source code
examples. All the sources are also available as separate files that you
can edit and compile (we will refer to these files as the source bundle).
Additionally, this section contains the rules and general guidelines that
apply to the course as a whole.
The latest version of this document along with the source bundle is
available both in the study materials in IS and on the student server
aisa:
• https://is.muni.cz/auth/el/fi/jaro2022/PB161/um/ – a PDF in
pb161.seminar.pdf and the source bundle in directories 01 through
12, t1 through t3 and sol – use the ‘download as ZIP’ option in the
sidebar to get entire directories in one go,
• log into aisa using ssh or putty, run pb161 update, then look under
~/pb161 (this chapter is in subdirectory 00).
We will update the files as needed, to correct mistakes or include additional
material. On aisa, running pb161 update at any time will update
your working copies, taking care not to overwrite your changes. It will
also tell you which files have been updated.
Part A.1: Course Overview
Welcome to PB161 Programming in C++. The course consists of lectures,
weekly seminars, programming tasks, and a programming test (exam)
at the end. Since this is a programming subject, most of the coursework
– and grading – will center around actual programming. You will write
a few tiny programs (15-20 minutes each) every week, a few bigger
programs (though still small, at a couple hundred lines each) during
the semester and there will be a simple (but strict) programming test
at the end (in the exam period) that you have to pass.
Writing programs is hard and consequently, this course will also be
hard – you absolutely need to put in effort to pass the subject. Hopefully,
you will have learned something by the end of it.
Further details on the organisation of this course are in this directory
or, if you are reading the PDF, in the following sections:
• 2_grading.txt – what is graded and how; what you need to pass,
• 3_tasks.txt – general guidelines that govern assignments,
• 4_reviews.txt – writing and receiving peer reviews,
• 5_quality.txt – code quality guidelines,
• 6_exam.txt – about the final programming exam,
• 7_plagiarism.txt – about cheating.
A.1.1 Topics The semester is organized as three four-week blocks.
Each week corresponds to a single chapter in this document, for a
total of 12 chapters. The study materials for each week are in directories
01 through 12 (one per week). Start by reading the introduction
(00_intro.txt in the ‘source’ version). Each block is followed by a set of
bigger tasks, in directories t1 through t3. Again, start by reading the
introduction (00_intro.txt) in there.
block topic lect. prep end
1 1. semantics 1, classes, … 15.2. 19.2.
2. semantics 2, lambdas, … 22.2. 26.2.
3. containers, algorithms 1.3. 5.3.
4. overloading, types, … 8.3. 12.3. 19.3.
2 5. operators, IO 15.3. 19.3.
6. RAII & exceptions 22.3. 26.3.
7. memory, unique_ptr 29.3. 2.4.
8. OOP 5.4. 9.4. 16.4.
3 9. templates 1 12.4. 16.4.
10. templates 2 19.4. 23.4.
11. iterators 26.4. 30.4.
12. review 3.5. 7.5. 14.5.
– 13. C++20 10.5. –
Part A.2: Grading Overview
There is a number of ways to obtain points:
max what notes
36pt tasks 3pt each, max 12
12pt code review 2pt each, max 6
12pt seminars 1pt/week: prep exercises + attendance
6pt sets 2pt extra for each set with 4+ points
3pt peer review 0.3pt per review, 10 reviews max
3pt activity 2pt + 1pt
18pt exam 3pt + 4pt + 5pt + 6pt
90pt total 72pt semester + 18pt exam
The semester maximum is 72 point. You need 40 points to pass the
semester (failing to do this means grade X). To pass the exam, you need
8 points on the exam. The final grade is then awarded as follows:
• [68, 90] points → A
• [63, 68) points → B
• [58, 63) points → C
• [53, 58) points → D
• [48, 53) points → E
• [40, 72] points → Z (if your ending type is ‘z’).
A.2.1 Seminars The preparatory exercises are to be worked out in the
corresponding week of the semester, with a deadline every Saturday at
midnight (see the semester overview in the previous section, column
‘prep’ for exact dates). Only the enclosed tests are executed upon submission,
and the result should appear in the corresponding notepad
within 5-10 minutes.
Together with seminar attendance, these exercises are worth a significant
fraction of what you need to pass the semester. You are awarded
a point for each unit (week) in which you submit at least 3 preparatory
exercises and attend1
the corresponding seminar in the following week.
1
If you cannot attend the seminar and file the requisite paperwork excusing you from attendance,
you can instead show original solutions for 3 of the r-type exercises from the affected
unit to your seminar tutor. If they are satisfactory, you will get a point as if you have attended
the seminar. Especially in case of an extended illness, you can also ask for an extension of
affected prep exercise submission deadlines. Be sure to do this as soon as you reasonably can.
PB161 Programming in C++ 2/114 June 28, 2022
In addition to gaining points, you may also get feedback and a chance
to discuss the submitted solutions in the seminar.
The activity points are likewise awarded in the seminar, in this case
for demonstrating the solution of one of the r-type exercises for the
week. These will be ‘live’ demos: you should solve the exercise on the
spot, without looking at a prepared solution (whether your own or
the reference one). You can do them from your own computer (using
pb161 beamer on aisa) or you can go to the front and use the teacher’s
computer. In any case, in addition to writing down a solution, you will
be expected to comment what and why you are doing. On the other
hand, the teacher will help you out if you get stuck in a blind alley.
You can do this twice during the semester: the first instance counts
as 2 points, the second as 1. If nobody else is interested, you can also
volunteer to do an exercise ‘for free’ (that is, if you already have your
3 activity points).
A.2.2 Programming Tasks In each block, there are 4 tasks of increasing
difficulty (both within and between blocks). There will be 8 deadlines
for each block, spread out over 6 weeks (there’s a deadline once
a week for the first month, then twice a week for another 2 weeks).
Most deadlines are on Saturday (same as weekly exercises), the 2 extras
are on Wednesdays. Submissions open 7 days before the first verity
deadline (that is 19.2., 26.3. and 23.4. – submissions done before these
dates will not be evaluated).
Each deadline gives you one chance to pass the automated test suite.
It does not matter when you pass any given task, but the test suite is
strictly binary: you either pass or you fail. More details and guidelines
are in 3_tasks.txt.
Verity tests continue to run after the last deadline: you can finish tasks
and still get results after they expire, but you will not get any points
for doing so. However, it does unlock peer reviews for the given task.
The deadline schedule is as follows:
week set 1 set 2 set 3
Wed Sat Wed Sat Wed Sat
1 26.2.
2 5.3.
3 12.3.
4 19.3.
5 23.3. 26.3. 26.3.
6 30.3. 2.4. 2.4.
7 9.4.
8 16.4.
9 20.4. 23.4. 23.4.
10 27.4. 30.4. 30.4.
11 7.5.
12 14.5.
13 18.5. 21.5.
14 25.5. 28.5.
A.2.3 Code Quality We should all strive to always write clean, readable
and well-designed code. Of course, this takes more time (often a
lot more time) than just going with the first thing that sort of works.
You will be able to submit six of your task solutions for teacher review.
Which assignments you choose to submit is up to you. Make sure that
you put in adequate effort to make the code as clean and nice as you
possibly can. The code must pass verity tests (within the designated
deadlines).
The last day on which you can file a request for (teacher) review is
3.4. for T.1, 1.5. for T.2 and 29.5. for T.3 (i.e. the day after the last test
deadline). Your teacher will have 10 days to complete the review.
• reviewer deadline: request + 10 days (i.e. 13.4., 25.5. and 8.6.)
• resubmit until 17.4., 15.5. and 12.6.
• earlier request → more time to fix stuff
With each review, you get a grade which corresponds to the following
point value:
• A = 2 points,
• B = 1 point,
• C = no points.
The detailed criteria for individual grades (and for code quality in general)
are provided in 5_quality.txt. If your grade is not A, your tutor
will point out what you need to improve.
You then get a chance (once) to improve your code and submit the task
for a second round of review. If your code has sufficiently improved,
you can get the next better grade (i.e. B if your first grade was C and A
if your first grade was B).
A.2.4 Peer Review Reading code is an important skill – sometimes
more so than writing it. While the space to practice reading code in this
subject is limited, you will be able to earn a few points doing just that.
The rules for peer review are quite different from those for teacher
reviews above:
• you can submit any code (even completely broken) for peer review,
• to write a review for any given submission, you must have already
passed the respective assignment yourself,
• there are no specific deadlines for requesting or providing peer
reviews.
It is okay to point out correctness problems during peer reviews, with
the expectation that this might help the recipient pass the assignment.
This is the only allowed form of cooperation (more on that below).
A.2.5 Examples A lot more work is available that what you need to
do, even for an A. We do not expect you to solve all the exercises nor
tasks – pick a subset you like, but be sure to spread the work through
the entire semester (there are very significant bonuses for doing it this
way). To give you an idea, there are some point calculations:
• below tables give achievable grades by passed task count,
• the specific grade in the range depends on the outcome of your
exam (8pt – 18pt),
• 4 tasks are the minimum to pass,
∘ all 3 sets must be covered,
∘ the 2 that are alone in their set must get 1pt or better review,
• 5 tasks are more or less the expected count,
• solving 6 tasks (i.e. half of them) allows considerable leeway in
other semester work,
• 6 tasks is also the minimum to get an A.
Maxing out all the optional work gives you this:
tasks pts rev other total grade
3 9 6 24 39 X
4 12 8 24 44 E-C
5 15 10 24 49 D-B
6 18 12 24 54 C-A
7 21 12 24 57 B-A
8 24 12 24 60 A
If you forfeit 2 weeks of seminars and the second ‘activity’ point and
get, on average, a B on teacher reviews, these are your prospects (you
do need to distribute work across task sets, to get the 2 point bonus on
all of them):
tasks pts rev other total grade
4 12 4 21 37 X
5 15 5 21 41 E-C
6 18 6 21 45 D-B
7 21 6 21 48 D-B
8 24 6 21 51 C-A
9 27 6 21 54 C-A
PB161 Programming in C++ 3/114 June 28, 2022
Part A.3: Task Sets
The general principles outlined here apply to all tasks. The first and
most important rule is, use common sense – the specifications are not
exhaustive and sometimes leave room for different interpretations. Do
your best to apply the most sensible one. Do not try to find loopholes
(all you are likely to get is failed tests). Technically correct is not the
best kind of correct.
Think about pre- and postconditions. Aim for weakest preconditions
that still allow you to guarantee the postconditions required by the
assignment. If your preconditions are too strong (i.e. you disallow
inputs that are not ruled out by the spec) you will likely fail the tests.
Do not print anything that you are not specifically directed to. Programs
which print garbage (i.e. anything that wasn’t specified) will fail
tests.
You can use the standard C++ library. External libraries or header
files are not allowed, unless specified as part of the assignment. Make
sure that your classes and methods use the correct spelling, and that
you accept and/or return the correct types. In most cases, either the
‘syntax’ or the ‘sanity’ test suite will catch problems of this kind, but
we cannot guarantee that it always will – do not rely on it.
If you don’t get everything right the first time around, do not despair.
The expectation is that most of the time, you will pass in the second or
third verity run (especially if you test your program carefully). If you
strongly disagree with a test outcome and you believe you adhered to
the specification and resolved any ambiguities in a sensible fashion,
please raise the issue in the discussion forum.
A.3.1 Submitting Solutions The easiest way to submit, for instance, a
solution to the task t1_cellular is this:
$ ssh aisa.fi.muni.cz
$ cd ~/pb161/t1
… edit files until satisfied …
$ pb161 submit t1_cellular
NB. Only the files listed in the assignment will be submitted and evaluated.
Please put your entire solution into existing files (or into files
you are instructed to create).
You can check the status of your submissions by issuing the following
command:
$ pb161 status
In case you already submitted a solution, but later changed it, you can
see the differences between your most recent submitted version and
your current version by issuing:
$ pb161 diff t1_cellular
The lines starting with - have been removed since the submission,
those with + have been added and those with neither are common to
both versions.
A.3.2 Compilation To compile and test your solution, use the make
command: each tX directory has a makefile in it. Typing make cellular
in this directory will first compile your solution into an executable
binary and then run clang-tidy, any tests you may have written, and
valgrind. If you want to work on your own computer instead of aisa,
you need to figure out the settings yourself. The makefile will tell you
which compiler we use and how we invoke it.
A.3.3 Evaluation There are three sets of automated tests which are
executed on the solutions you submit. The first set is called ‘syntax’
and runs immediately after you submit. Only 2 checks are performed:
the code compiles and it passes clang-tidy.
The next step is ‘sanity’ and runs every midnight and noon. Its main
role is to check that your program meets basic semantic requirements,
e.g. that it recognizes correct inputs and produces correctly formatted
outputs. The ‘sanity’ test suite is for your information only and does
not guarantee that your solution will be accepted. The ‘sanity’ test
suite is only executed if you passed ‘syntax’.
The ‘verity’ test suite covers most of the specified functionality and
runs once or twice a week (the exact schedule is in the previous section).
If you pass the verity suite, the assignment is considered complete and
you are awarded the points. The verity suite will not run unless the
code passes ‘sanity’ (with the exceptions specified in the task descriptions).
Please note that any memory errors (including memory leaks,
as reported by valgrind) will cause ‘verity’ to fail.
Only the most recent submission is evaluated, and each submission
is evaluated at most once in the ‘sanity‘ and once in the ‘verity’ mode.
You will find your latest evaluation results in the IS in notepads (one
notepad per task).
Part A.4: Peer Reviews
You can optionally participate in peer reviews, both as a reviewer and
as a review recipient. While reviewers get points for their effort, the
recipients do not – instead, they get (hopefully) useful information.
A.4.1 Requesting Reviews If you would like to have your code reviewed,
you can issue the following command:
$ pb161 review --request t1_cellular
Substitute other programming tasks for t1_cellular as appropriate.
You can request a peer review on a task which you did not pass yet.
You may get up to 3 reviews for any given request. The reviewer
will work with the submission that was current at the time you have
created the request. Make sure you submit the code you want reviewed
before requesting the review.
The pb161 update command will indicate whether someone reviewed
your code, by printing a line of the form A reviews/t1_cellular.by.xlogin.
To read the review, look at the files in ~/pb161/reviews/t1_cellular.by.xlogin
– you will find a copy of your submitted sources along
with comments provided by the reviewer. After you read your review,
you should write a few sentences for the reviewer into note.txt in the
review directory (please wrap lines to 80 columns) and then run:
$ pb161 review --accept 100
Instead of 100, you can use a smaller number, indicating what percentage
of the points the reviewer deserves for their job. Please make sure
that you grade the review honestly – the reviews will be screened for
abuse and depending on the type of misconduct, one or both parties
will be punished.
To request a review from a teacher (as opposed to peer review), add
--teacher to the command:
$ pb161 review --request t1_cellular --teacher
The output from pb161 status will indicate the task submissions for
which you have requested a teacher review.
A.4.2 Writing Reviews To participate as a reviewer, start with the
following command:
$ pb161 review --list
You will get a list of review requests for which you are an eligible
reviewer. In particular, only tasks that you have already successfully
solved will show up. If you like one of the entries, note its number (e.g.
7) and type:
$ pb161 review --checkout 7
$ cd ~/pb161/reviews/
$ ls
There will be a directory for each of the reviews you agreed to write.
PB161 Programming in C++ 4/114 June 28, 2022
Each directory contains the source code submitted for review, along
with further instructions (the file readme.txt).
When inserting your comments, please use double ** to make the
comment stand out, like this:
/** A short, one-line remark. **/
or for longer comments:
/** A longer comment, which should be wrapped to 80 columns or
** less, and where each line should start with the ** marker.
** It is okay to end the comment on the last line of text like
** this. **/
Part A.5: Code Quality
As mentioned earlier, when you submit your code for teacher review,
it will be graded A–C. The following criteria apply.
A.5.1 Vices This is a list of things your code should not do, and the
best grade that is possible if they make an appearance. In all cases, only
‘nontrivial’ instances matter, but unfortunately, there is no obvious
line between trivial and nontrivial. Your reviewer’s judgment will
apply.
• Code duplication: this is a very serious problem, both when the
code is literal copy&paste and when there are minor modifications
between the copies. Any significant duplication is an automatic C.
Code which is highly redundant (multiple implementations of the
same concept or pattern, even if not literally copied) is still a problem,
including duplication of the standard library. All but trivial cases
warrant a C.
• Spaghetti: another common and very serious problem, often paired
with the previous. Long functions, an excessive number of local
variables, non-obvious side effects which affect control flow down
the line, functions which do too many things at once. A minor
instance caps your grade at B, anything more than that means a C.
• Bad naming caps your grade at B (if the problem is pervasive, a C is
very likely). This includes:
∘ meaningless names – single-letter global variables, names which
say nothing about the purpose of the thing (tmp1 through tmp7,
tmp, tmptmp, pom, pomoc, …),
∘ names which are not English nor established placeholders or
abbreviations (these are fine: a, b for arguments of binary operators,
i, j for loop variables, etc.),
∘ overlong, completely redundant names for local objects
(first_plus_operand, loop_index_variable_1).
• Inappropriate data types, data structures or algorithms: using building
blocks which do not fit the intended purpose makes programs
hard to follow and reason about, and often also leads to poor performance.
Abuse of strings is especially common. Caps the grade
at B (but may contribute strongly to a C).
If your code is free of the above vices, it will get a B or an A, depending
on the virtues described below.
A.5.2 Virtues To earn a grade better than C, your code should be free
from vices and also demonstrate some of the following virtues.
• Cohesion and orthogonality: each code unit (class, function, …) does
one well-defined thing and has a clear and fitting name. Required
for A.
• Good naming: names should be clear, descriptive, respect word
categories (based around verbs for functions and nouns for types
and variables), be free from spelling or grammatical errors. Names
should not be redundant – context matters. The verbosity of a
name should be inversely proportional to its scope. Do not repeat
established context (no list::list_length). Required for A.
• Comments: each non-obvious code unit should have a comment
concisely describing what it does and why. Contributes towards an
A, but is not required. Comments which establish correctness of
the code are especially valued.
• Preconditions: each function should clearly state its preconditions,
preferably in executable form (assert). Contributes significantly
toward an A.
Part A.6: Exam
The raison d’être of this course is to teach you to write correct C++
programs on your own – and the programming test is designed to ensure
that this was indeed the outcome for you personally. Of course,
we recognize that there is additional pressure when you are programming
for an exam. You will get plenty of time to solve the exercises (in
relation to their difficulty).
During the exam, it’ll be possible to submit the solutions and get back
results of a ‘sanity’ test. The ‘sanity’ assertions will also be included
with the exam source files, for your convenience. There is no requirement
to pass clang-tidy.
The exam will take place on 31st of May and 2nd of June (Tuesday and
Thursday, respectively) starting at 12:30 and will extend until 17:00.
Additional attempts will be possible on 14th and 28th of June. You
will get a ‘yes/no’ verity result (without any indication of what went
wrong) at 14:00 and 15:30, and full results at 17:00.
You will also get a chance for a ‘rehearsal’: there are two practice exams
in an appendix of this document (directory pex). You can work them
out and submit them for evaluation, as if they were a real exam. This
is strictly optional and will not be graded in any way. It is up to you to
complete them within a reasonable time limit (e.g. 3 hours, 2/3 of the
official time limit for the real exam) and on your own.
You can submit multiple times for the practice tests and get ‘verity’
test results immediately, but please keep in mind that this will not be
possible at the actual exam.
A.6.1 Evaluation The programming test will be evaluated using automated
tests, just like the 12 ‘major’ tasks. Each exercise is evaluated
in a binary fashion: you must pass all tests in order to succeed on the
given task, in which case you are awarded its points.
If you fail to obtain 8 points (i.e. pass 2 out of the 4 exercises), you get an
F and you can try again according to the standard rules for repeating
exams.
A.6.2 Materials The exam will be offline. The exam computers will
have a standard selection of text editors and development tools2
installed,
in their default configurations. This document (but without
exercise solutions) and lecture slides (again without example source
code) will be available for reference.
Part A.7: Plagiarism
tl;dr: Please work alone and do not cheat. Cheating is a colossal waste
of everyone’s time. We would prefer to spend that time on improving
the course for everyone. Thank you.
And now for the long version, because sadly, the above is not enough.
The goal of this subject is to teach you to write programs in C++ –
from understanding the problem, through designing the solution and
writing it down in C++. You must be able to do all of this on your own.
Teamwork has its place, but it’s not in this subject.
You must work out all graded exercises and tasks entirely on your own.
Discussing the solution, even in abstract terms, is not permitted. If
you do not understand something, ask your tutor privately. If you are
caught cheating, ‘we have only shared ideas’ or even ‘we only discussed
2
You can expect VS Code, Geany, micro and vim to be present. Qt Creator might be available.
CLion has been excluded due to stability issues (we don’t want to deal with any more crashes
in the middle of an exam than we absolutely have to).
PB161 Programming in C++ 5/114 June 28, 2022
the problem statement’ will not hold as a valid defence. If you want
to study together, that is fine, and encouraged – there are plenty of
ungraded exercises for this purpose. You can discuss those, solve them
together, share and compare your solutions and so on.
Please note that you are also responsible for keeping your solutions
private. If you only use the pb161 command on aisa, it will make your
~/pb161 directory inaccessible to anyone else (this also applies to schoolprovided
UNIX workstations). Keep it that way. If you work on your
solution using other computers, make sure they are secure. Do not
publish your solutions anywhere (on the internet or otherwise) and do
not share them for any reason. All parties in a copying incident will
be treated equally.
A.7.1 Penalties Any points awarded for work that has been shared
with another student are voided (including any points from reviews,
and any other bonuses they enabled – that is, if you copy a prep exercise
and you had been awarded a point for that week’s seminar, that point
will be revoked). Additionally, following penalties apply:
items copied penalty total
1st task -3pt -3pt
2nd task -5pt -8pt
3rd task -7pt -15pt
1st prep ex. -1pt -1pt
2nd prep ex. -2pt -3pt
3rd prep ex. -3pt -6pt
4th prep ex. -5pt -11pt
The ‘counter’ is shared between tasks and exercises (with tasks coming
first), so if you copy (or let someone copy, same thing) a task and two
exercises, that’d be -3 (1st task) + -2 (2nd exercises) + -3 (3rd exercise),
for a total of -8pt.
Part 1: Strings and Classes
Welcome to PB161. If you haven’t read the rules and guidelines in
Part A (directory 00 in the source bundle), please do so now, before
going on.
The exercises this week will look at some of the basics that you have
seen in the lecture: strings, dynamic arrays – std::vector, classes with
methods, and const references. These concepts are further explored
in the ‘demonstrations’ (commented examples; please note that these
do not replace the lectures – they are meant to be complementary).
The corresponding files in the source bundle are named d?_*.cpp, i.e.
d1_fibonacci.cpp through d4_lemmings.cpp.
1. fibonacci – using std::vector (dynamic array)
2. hamming – introduction to std::string
3. hero – introduction to object composition
4. lemmings – collections of custom objects
The second part of the study materials for each week gives you a couple
of ‘elementary’ exercises, which you should be able to quickly solve to
make sure you understand the concepts from the lecture and from the
commented examples above. Sample solutions are in Part S at the end
of the PDF, or in the directory sol in the source code bundle. Please
note that the sample solution is not always the simplest possible – it’s
fine to take a more roundabout approach. The source files for this
section are named e?_*.cpp.
This week, the elementary exercises are:
1. predicates – properties of lists of numbers
2. palindrome – checking that an std::string is a palindrome
3. pascal – fill in an std::vector
The next section has slightly more difficult exercises. These are labelled
preparatory, since they exist to let you prepare for the corresponding
seminar. You are strongly encouraged to solve at least 3 of them every
week (if you submit them by Saturday, you can then gain a point for
attending the seminar). The respective source files in the bundle are
called p?_*.cpp. Note: Discussing and sharing solutions is strictly forbidden
– you must solve the exercises on your own. For details, see
Part A (directory 00 in the source bundle).
1. counting – count words and lines in a string
2. fraction – evaluate a continued fraction
3. words – break a string into a vector of one-word strings
4. account – encapsulation of state, const methods
5. shapes – object composition
6. contacts – collections of your own objects
The last section has regular exercises – those will be (on average) yet
more difficult and let you further practice programming with the concepts
that you have learned this week. Like with elementary exercises
earlier, solutions to these can be freely discussed and shared, you can
work on the exercises with your friends, and you can compare your
solution to those included in Part S. Some of these exercises will be
solved interactively in the seminar. The files are named r?_*.cpp.
1. wrap – wrap long lines into paragraphs of a given width
2. digits – representing numbers in a positional system
3. sieve – find prime numbers
4. bsearch – binary search in a sorted std::vector
5. qsort – the staple of in-place sorting algorithms
6. radix † – a fast comparison-free sorting algorithm
Part 1.a: Using the source bundle
We recommend that you work on aisa, which has all the required
tools installed and set up correctly. You can use micro as your editor if
you are not familiar with vim, or you can use a remote editing feature
in your code editor of choice. If you prefer to set up your own, local,
environment, you are of course free to do that, but please keep in mind
that your tools are your responsibility.
If you work on aisa, you can check your solutions against the test cases
provided with the exercises by running make (this tries to compile all
of them in order) or make p1_counting to compile and test only one of
them. Additionally, make will run your code through clang-tidy and
valgrind.
When you are satisfied with the solution, you can use pb161 submit
in the directory of the particular unit. This week, that’s ~/pb161/01.
You can consult pb161 status to confirm that your submission is in the
system. Thus, the entire sequence looks like this:
$ pb161 update
$ cd ~/pb161/01
… edit code until tests pass / you are satisfied …
$ pb161 submit
$ pb161 status
You can see test results in the notepads in the IS. As an alternative, you
can use the following command to submit the solution and display the
test results as soon as they become available:
$ pb161 submit --wait
Part 1.d: Demonstrations
1.d.1 [fibonacci] We will assume some familiarity with C (or at least
some C-style braces-and-semicolons language, like Java). First things
PB161 Programming in C++ 6/114 June 28, 2022
first: subroutines, statements, types and values. In C++, variables,
containers and so on hold values. Assignment updates those values
and does not rebind the name to a different object. If you come from
Java or Python, this is a bit of a culture shock. See also lectures.
In this demo, we will implement the mother of all programming language
examples, the Fibonacci sequence (forget hello world, this is not
that kind of a course). First the function (subroutine) signature – in
order come:
• return type – in this case std::vector< int >, then
• the name of the subroutine – fibonacci, and finally
• the argument list: int n.
std::vector< int > fibonacci( int n )
A vector is a sequence container – it holds a sequence of values. In
C++, containers are generic, that is, parametrized by the type of their
elements, and these type parameters are specified in angle brackets. In
this case, we are declaring that fibonacci returns a vector (sequence)
of integers (int is the ‘default’ integer type in C++). The curly braces
after the signature enclose the function body.
{
The body is a sequence of statements, separated by semicolons (with
the exception of compound statements – which are enclosed in braces
and are not followed by a semicolon). The first statement in this function
is a local variable declaration, which consists of the type (the already
familiar std::vector< int >), possible declarators (like pointers
and references… again, we will get to those later – there are none in
this particular case) and the name of the variable: fib.
std::vector< int > fib;
Vectors are generalized arrays: unlike traditional C arrays, they can be
resized on demand. To set the size of a vector, we can use its method
resize: to call a method of an object (and vector is an object), we use
the following syntax:
• the variable holding the object – fib, then
• a dot,
• then the name of the method to call,
• then an argument list, enclosed in parentheses.
Of course, like everything in C++, method calls can get a lot more
complicated, and it is a topic that we will likewise revisit.
fib.resize( n, 1 );
Now that fib is an appropriately sized vector, with the number 1 stored
at each index, we can go on to rewrite the values to the actual Fibonacci
sequence. We will use a for loop, which you probably know from C –
the for statement has 3 sections enclosed in parentheses and separated
by semicolons:
• initialisation, which usually declares or initializes the loop variable,
• the loop condition,
• the iteration expression, which is executed after every iteration,
before the loop condition.
The head of the loop is followed by a statement, which is the body: the
code that is repeatedly executed. Often, this is a compound statement
(enclosed in braces) but it doesn’t have to.
for ( int i = 2; i < n; ++ i )
In this case, the body consists of a single statement: an assignment,
which updates the i-th position in the vector fib with the sum of the
values stored at the two preceding indices. Square brackets after a
variable name indicate the indexing operator and works analogously
to array indexing in C.
fib[ i ] = fib[ i - 1 ] + fib[ i - 2 ];
The return statement does two things, like in most imperative languages:
it provides the return value, and it immediately stops execution
of the function, transferring control back to the caller.
return fib;
}
All demonstrations and exercises in this collection contain a short
collection of test cases. In the demos, they usually serve to show how
the code explained in the main part works, and for you to change and
experiment.
int main() /* demo */
{
std::vector fib_7{ 1, 1, 2, 3, 5, 8, 13 };
std::vector fib_1{ 1 };
assert( fibonacci( 7 ) == fib_7 );
assert( fibonacci( 1 ) == fib_1 );
}
1.d.2 [hamming] Besides sequences of numbers, another type of sequence
frequently appears in computer programs: strings, which are
made of letters. In C++, the basic data type for working with strings is
std::string, and it is rather similar to a vector, though strings provide
additional methods, for operations commonly performed on strings
(but not so commonly on other sequences).
In this demo, we will show some basic usage of std::string. The following
function, called hamming returns an integer (of type int) and
accepts 2 arguments. Notice that there are some new elements in the
declarations of those arguments: the const qualifier, meaning that we
do not intend to modify the values a and b, and a reference declarator,
denoted &.
These two often go together – in this arrangement, they declare a
constant reference. In a function argument list, this means that the
data will not be copied when the function is called, but the function
promises not to change the original. Since a string might contain a
lot of data, copying all of it might be expensive: this is why we prefer
to use a constant reference to pass it into a function, if the function
only needs to examine, but not change, the content of the string. In
other words, a and b are not values in their own right; instead, they are
aliases (new names) for existing values, albeit such that the original
values cannot be modified through these new names. If you try to, the
compiler will complain.3
int hamming( const std::string &a, const std::string &b )
{
First, we declare a precondition: the strings must be of equal size.
In other words, calling hamming on two strings of different length is
a programming error: the caller is responsible for ensuring that the
condition holds.
assert( a.size() == b.size() );
We declare a local variable to hold the computed distance, of type int
(the ‘default’ integral type in C++).
int distance = 0;
Again, a standard C-style for loop. Notice that strings can be indexed,
just like arrays and vectors. Also notice that the loop variable is now
of type size_t – an unsigned integer type. This is because the size
3
Of course, this being C++, there is a way around that. It is only needed very rarely, and only
in ‘plumbing’ – low-level code which implements, for instance, new data types.
PB161 Programming in C++ 7/114 June 28, 2022
methods of standard containers in C++ return unsigned numbers,²
and comparing signed and unsigned integers can cause problems.
for ( size_t i = 0; i < a.size(); ++ i )
if ( std::toupper( a[ i ] ) != std::toupper( b[ i ] ) )
distance ++;
And a return statement.
return distance;
}
That is all. If you have never heard of Hamming distance before, it
might be a good idea to look it up.
int main() /* demo */
{
assert( hamming("Python", "python") == 0 );
assert( hamming("AbCd", "aBcD") == 0 );
assert( hamming("string", "string") == 0 );
assert( hamming("aabcd", "abbcd") == 1 );
assert( hamming("abcd", "ghef") == 4 );
assert( hamming("Abcd", "bbcd") == 1 );
assert( hamming("gHefgh", "ghefkl") == 2 );
}
² Arguably, this is a design mistake in C++. There are proposals to fix
it, but a change in this regard is going to take a long time, if it ever
happens. In the meantime, it makes sense to use unsigned types for
straightforward loop variables (i.e. those that count up).
1.d.3 [hero] In many programs, pre-made data types included in the
standard library are more than sufficient. However, it is also often the
case that a custom data type could be useful – most often to describe a
particular concept from the domain which the program models.
Let us consider a dungeon crawler, or some other role-playing game
set in a fantasy world. In such games, the protagonist will be able to
pick up items and make use of them, for instance wield a sword to fight
the critters in the dungeon.
This would be a rather typical use case for a custom data type: there
might be many individual swords in the game, but they all share the
same essential set of attributes, like weight, or the amount of damage
they deal to the opponent. Of course, we could store these attributes
as a tuple, with anonymous fields, and remember that the weight is
the first element and the attack strength is the second. While fine in a
small program, this approach is not very scalable.4
With struct (and class, in a short while), we can create user-defined
data types, with named attributes and methods. The struct keyword
is inherited from C, where it defines an aggregate (or record) data type.
C++ extends this concept with methods, constructors, destructors, inheritance,
and so on. However, at their heart, C++ objects are really
just fancy record types. We will start by exploring these.
A record type describes a composite (or aggregate) value, made of a
fixed number of attributes (fields), possibly of different types. In this
sense, it is very much like a tuple. However, in a record type, the
fields have names, and their values are accessed by using those names
(instead of their positions as in a tuple). To define a record type, we use
the keyword struct, followed by the name of the type, followed by the
definition of the individual fields. Let’s start by defining a type which
will describe a sword.
struct sword
{
The most important attribute of a sword is, clearly, a fancy name.
4
After all, we could just use void pointers, remember how big the data is and which attribute
is stored at which offset. There is a good reason why nobody writes serious programs in this
style.
Recall that we can use std::string to conveniently store strings. Let
us then declare the attribute name of type std::string:
std::string name;
Then there are some attributes that deal with game mechanics. Let
us just describe them using two integers, weight and attack. In actual
games, things usually get a bit more complicated. It is possible to give
default values to attributes – in this case, when a value of type sword is
created, weight and attack will be both set zero. How this is achieved
or why it is important will be discussed later.
int weight = 0;
int attack = 0;
};
That is all. At this point, sword is a type, like int or std::string, and we
can declare variables of type sword, return values of type sword from
functions, or pass values of type sword as function arguments. For
example, let’s write a trivial predicate on values of type sword. Notice
the syntax for attribute access: it is the same that we have used for
calling methods of ‘built-in’ types like std::string earlier. This is not a
coincidence.
bool sword_is_heavy( const sword &s )
{
return s.weight > 50;
}
Let us define another record type, shield, before moving on.
struct shield
{
std::string name;
int weight = 0;
int defense = 0;
};
Swords and shields are usually rather passive. However, programs often
also model more dynamic entities; user-defined record types would
seem like a good fit to describe their static side (i.e. their attributes).
For instance, a hero would have a health bar (how much damage they
can take before dying), and some weapons (a sword and a shield, for
instance). And obviously a name.
Given a record type which models an entity, it is possible, of course,
to write functions which describe the behaviours of this entity. For
instance hero_walk or hero_attack could be functions which take the
specific hero to act on as one of their arguments.
You perhaps notice the imbalance though: attributes use a nice and
concise syntax, value.attribute, but functions use much clumsier
type_method( value, … ). But we did not have to say string_size(
string ) earlier.
Indeed, in C++, it is possible to also bundle functions into user-defined
data types, in addition to attributes. Such data types are no longer
called ‘record types’ – instead, they are known as classes. In other
words, a C++ class is a user-defined data type with attributes and methods
(associated functions). Let us define one of those – the syntax is
analogous to record types:²
class hero
{
In classes, attributes are often private: only methods of the same class
are allowed to directly access them. This is the default: unlike struct,
when we start writing declarations into a class, they will be inaccessible
to the outside code. This is okay for our current purposes. It is also
common practice to prefix attributes in a class (unless they are public)
with an underscore, or some other short string (m_, for member, is also
sometimes used), to avoid naming conflicts: it is not allowed to have
an attribute and a method with the same name.
PB161 Programming in C++ 8/114 June 28, 2022
std::string _name;
shield _shield;
sword _sword;
To mark further attributes and methods as accessible to the outside
world, we use the label public, like this:
public:
Methods are declared just like functions, the only immediate difference
being that this is done inside a class. And the odd const keyword at
the end of the signature. This const tells the compiler that the method
does not change the object in any way when it is called (again, this is
enforced by the compiler).
bool wields_heavy_sword() const
{
return sword_is_heavy( _sword );
}
An example of non-const method would be the following, which causes
the hero to wield a sword given by the argument. The method assigns
into one of the attributes, which obviously changes the object, and
hence cannot be marked const.
void wield( const sword &s )
{
_sword = s;
}
Finally, we will add a constructor: a special kind of method which is
called automatically by the compiler whenever a value of type hero is
created, e.g. by declaring a local variable. The constructor’s name is the
name of the class, and it has no return type, bit it can have arguments.
Unlike standard functions (and standard methods), constructors have
an initialization section, which can initialize attributes, e.g. by passing
arguments to their constructors. When the body of the constructor
is entered, all the attributes will have been already constructed. The
initialization section starts with a colon, and is followed by a list of
expressions of the form attribute( argument list ).
hero( std::string name )
: _name( name )
{}
};
That is quite enough for now. Let us look at a few examples of code
using the above types.
int main() /* demo */
{
sword katana = { "Katana", 10, 17 };
hero protagonist( "Hiro Protagonist" );
protagonist.wield( katana );
assert( !protagonist.wields_heavy_sword() );
}
² In fact, struct and class are essentially the same thing, and only differ
in minor syntactic details. Nonetheless, we will usually write struct
for plain record types (without methods) and class for actual classes.
1.d.4 [lemmings] While we are talking about computer games, you
might have heard about a game called Lemmings (but it’s not super
important if you didn’t). In each level of the game, lemmings start
spawning at a designated location, and immediately start to wander
about, fall off cliffs, drown and generally get hurt. The player is in
charge of saving them (or rather as many as possible), by giving them
tasks like digging tunnels, or stopping and redirecting other lemmings.
Let’s try to design a class (reminder: a class is a user-defined data type
with attributes and methods) which will capture the state of a single
lemming:
class lemming
{
Each lemming is located somewhere on the map: coordinates would
be a good way to describe this. For simplicity, let’s say the designated
spawning spot is at coordinates (0, 0).
double _x = 0, _y = 0;
Unless they hit an obstacle, lemmings simply walk in a given direction
– this is another candidate for an attribute; and being rather heedless,
it’s probably good idea to keep track of whether they are still alive.
bool _facing_right = true;
bool _alive = true;
Finally, they might be assigned a task, which they will immediately
start performing. An enumerated type is another kind of a userdefined
type and consists of a discrete set of named labels. You have
most likely encountered them in C.
enum task { no_task, digger, stopper, /* … */ };
task _task = no_task;
public:
Let us define a couple methods:
void start_digging() { _task = digger; }
bool busy() const { return _task != no_task; }
bool alive() const { return _alive; }
void step()
{
_x += _facing_right ? 1 : -1;
_y += 0; // TODO gravity, terrain, …
}
};
Earlier, we have mentioned that user-defined types are essentially
the same as built-in types – their values can be stored in variables,
passed to and from functions and so on. There are more ways in which
this is true: for instance, we can construct collections of such values.
Earlier, we have seen a sequence of integers, the type of which was
std::vector< int >. We can create a vector of lemmings just as easily:
as an std::vector< lemming >. Let us try:
int count_busy( const std::vector< lemming > &lemmings )
{
Note that the vector is marked const (because it is passed into the function
as a constant reference). That extends to the items of the vector:
the individual lemmings are also const. We are not allowed to call
non-const methods, or assign into their attributes here. For instance,
calling lemmings[ 0 ].start_digging() would be a compile error.
int count = 0;
Now is perhaps a good time to introduce a new piece of syntax: the
range for loop. Its main purpose is to iterate over all items in a given
collection, which is exactly what we want to do. It consists of a declaration
of the loop variable, followed by a colon, and an expression
which ought to yield an iterable sequence.
for ( const lemming &l : lemmings )
if ( l.busy() )
count ++;
return count;
}
int main() /* demo */
{
PB161 Programming in C++ 9/114 June 28, 2022
We first create an (empty) vector, then fill it in with 7 lemmings.
std::vector< lemming > lemmings;
lemmings.resize( 7 );
We can call methods on the lemmings as usual, by indexing the vector:
lemmings[ 0 ].start_digging();
assert( count_busy( lemmings ) == 1 );
We can also modify the lemmings in a range for loop – notice the
absence of const; this time, we use a mutable reference (often called
just a reference, or an lvalue reference – more on that later):
for ( lemming &l : lemmings )
{
assert( l.alive() );
l.start_digging();
}
assert( count_busy( lemmings ) == 7 );
}
Part 1.e: Elementary Exercises
1.e.1 [predicates] Write the following predicates (pure functions
which return a boolean value). The first two return true if all (all_odd)
or at least one (any_odd) number in the list is odd:
bool all_odd( const std::vector< int > & );
bool any_odd( const std::vector< int > & );
The third returns true if there are at least n numbers divisible by k:
bool count_divisible( const std::vector< int > &, int k, int n );
1.e.2 [palindrome] Write a predicate which decides whether a given
string is a palindrome, i.e. reads the same in both directions.
bool is_palindrome( const std::string &s );
1.e.3 [pascal] Write a function which builds the n-th row of Pascal’s
triangle as a vector of integers and returns it.
std::vector< int > pascal( int n );
Part 1.p: Preparatory Exercises
1.p.1 [counting] In this exercise, we will work with strings in a readonly
way: by counting things in them. Write two functions, word_count
and line_count: the former will count words (runs of characters without
spaces) and the latter will count the number of non-empty lines.
Use range for to look at the content of the string.
Here are the prototypes of the functions – you can simply turn those
into definitions. We pass arguments by const references: for now,
consider this to be a bit of syntax, the purpose of which is to avoid
making a copy of the string. It will be explained in more detail later.
Also notice that in a prototype, the arguments do not need to be named
(but you will have to give them names to use them).
int word_count( const std::string & );
int line_count( const std::string & );
1.p.2 [fraction] Write a function which evaluates a continued fraction:
given a vector of coefficients of the continued fraction, it computes
a numerator and a denominator of a traditional fraction with
the same value.
A continued fraction is a representation of a rational number q as a sum
of a0 and the reciprocal of a second number, q0, which is itself written
as a continued fraction: q0 = a0 + 1/q1 where q1 = a1 + 1/q2, q2 =
a2 + 1/q3 and so on. The sequence a0, a1, a2, … are the coefficients of
the continued fraction. For a rational number, one of the qn eventually
becomes 0 and the sequence ends there.
For more details, see e.g. wikipedia.
Define a traditional fraction as a struct with two integer attributes, p
and q (the numerator and the denominator, respectively).
struct fraction;
fraction eval_continued( const std::vector< int > &coeff );
1.p.3 [words] Write a function that breaks up a string into individual
words. We consider a word to be any string without whitespace (spaces,
newlines, tabs) in it.
Since we are lazy to type the long-winded type for a vector of strings,
we define a type alias. The syntax is different from C, but it should be
clearly understandable. We will encounter this construct many times
in the future.
using string_vec = std::vector< std::string >;
The output of words should be a vector of strings, where each of the
strings contains a single word from in.
string_vec words( const std::string &in );
1.p.4 [account] In this exercise, you will create a simple class: it will
encapsulate some state (account balance) and provide a simple, safe
interface around that state. The class should have the following inter-
face:
• the constructor takes 2 integer arguments: the initial balance and
the maximum overdraft
• a withdraw method which returns a boolean: it performs the action
and returns true iff there was sufficient balance to do the with-
drawal
• a deposit method which adds funds to the account
• a balance method which returns the current balance (may be negative)
and that can be called on const instances of account
class account;
1.p.5 [shapes] Another exercise about objects, this time about their
composition. We will write 2 classes: point and rectangle. Points have
2 coordinates (x and y) and rectangles are defined by 2 points (their
opposing corners).
Points are constructed from two doubles: the x and y coordinates, and
they have x() and y() methods which return doubles.
class point;
A function to compute euclidean distance between two points. Writing
it is a part of the exercise, but it will be also useful when implementing
the diagonal method in rectangle.
double distance( point a, point b );
Rectangles are constructed from a pair of points (bottom left and upper
right corner) and provide methods: width, height and diagonal which
all return a double, and a method center which returns a point.
class rectangle;
1.p.6 [contacts] We will look at using collections of objects. We only
know one type of collection: a dynamic array, so that’s what we will
use. The objects we will consider are simple entries in a contact list:
they have a name and a phone number (both stored as strings).
We need contact to possess a two-parameter constructor (which initializes
both its fields) and two getters (methods), name and phone.
class contact;
using contacts = std::vector< contact >; /* type alias */
PB161 Programming in C++ 10/114 June 28, 2022
Let’s write a helper function which checks whether the string small is
a prefix of the string big.
bool is_prefix( const std::string &small, const std::string &big );
And finally, a function to return all contacts whose names start with
the given prefix (use is_prefix in a loop).
contacts search( const contacts &list, const std::string &prefix );
Part 1.r: Regular Exercises
1.r.1 [wrap] We will look at std::string again. Our first task will be to
implement a simple word wrapping (paragraph filling) algorithm.
Input: An std::string with ASCII text (letters, spaces, newlines and
punctuation) and columns (a number of columns). Each line of the input
text represents a single paragraph.
Output: A string in which there are actual paragraphs with line breaks,
not too far after the given column number. That is, at most a single
word crosses the column-th column. Newlines in the input are replaced
by double newlines in the output.
std::string fill( const std::string &in, int columns );
1.r.2 [digits] Write a function to convert a number into its positional
representation in a given base. Return the result as a vector, with the
most significant digit first.
std::vector< int > digits( int n, int base );
1.r.3 [sieve] Implement the Sieve of Eratosthenes for quickly finding
the largest prime smaller than or equal to a given bound.
int sieve( int bound );
1.r.4 [bsearch] Implement binary search on a vector. In this case, we
will use a non-const reference to pass the vector, because we don’t
know yet how to deal with const iterators properly. We also don’t
know how to write generic algorithms (we will see that at the end of
this course), so we use a vector of integers.
It is customary to return the end iterator if an element is not found.
A pair of iterators in C++, by convention, denotes a left-closed / rightopen
interval, like this: [begin, end).
std::vector< int >::iterator bsearch( std::vector< int > &vec, int
val );
1.r.5 [qsort] Implement recursive quicksort on a vector of integers.
The algorithm proceeds as follows:
1. if the array has 0 or 1 element, it is already sorted: stop,
2. otherwise select one of the elements as a pivot,
3. rearrange the vector (array) into two smaller partitions, such that
all items smaller than the pivot go into the left partition, then comes
the pivot, then the right partition with the remaining (greater or
equal) elements,
4. recursively quicksort the left and the right partition (excluding
the pivot).
Useful invariant: after each partition, the pivot is at its correct index
in the final sorted order.
See also: https://xkcd.com/1185/
void quicksort( std::vector< int > &vec );
1.r.6 [radix] † Most sorting algorithms that you encounter are socalled
‘comparison sorts’: they perform pairwise comparisons to determine
the correct order of elements. It is a well-known result that an
optimal sort of this type will perform O(nlogn) comparisons.
However, many types of data have additional properties which make
linear-time – O(n) – sorting possible. One such algorithm is radix sort
and it works for numbers and strings. In this exercise, we will use it to
sort numbers.
Like quicksort, the algorithm has 2 basic components: a helper function
sort_by_digit which performs a stable sort only looking at a i-th digit
(letter) in each of the numbers (strings). This can be done in linear time
because there is only a fixed number of digits (or letters):
1. in one pass, count the number of keys for each possible value of
the given (i-th) digit,
2. in a second pass, sort the input into pre-determined buckets (filling
the buckets in the iteration order, ensuring stability of the sort).
The buckets are then concatenated to form the digit-sorted sequence
(though they can also be allocated as a consecutive block upfront, saving
a temporary copy).
The main procedure then simply performs sort_by_digit on each digit,
starting from the least significant. The result is a sorted array.
void radixsort( std::vector< unsigned > &to_sort, int base = 10 );
Part 2: References and Lambdas
In this chapter, we will work with references (both constant and mutable)
and also look at the basics of higher-order functions in C++.
Demonstrations:
1. stats – input and output parameters
2. primes – fill in a vector with prime numbers
3. iterate – building sequences by iterating a function
4. newton – a general routine for numeric approximation
Elementary exercises:
1. fibonacci – old sequence, new function signature
2. normalize – divide out the gcd from a fraction
3. accumulate – sum up f(x) for all x in an std::vector
Preparatory exercises:
1. rewrap – word wrapping redux, this time in-place
2. golden – basic uses of output parameters
3. divisors – collections as in/out parameters
4. midpoints – in/out parameters of custom types
5. higher – higher-order function primer: map and zip
6. fixpoint – find a fixed point of a monotonic function
Regular exercises:
1. euler – implement Euler’s totient function φ
2. approx – somewhat easier approximation
3. solve – a very simple game solver
4. sort – selection sort with a comparator
5. permute – compute a vector of digit permutations
6. bsearch – binary search with a comparator
Part 2.d: Demonstrations
2.d.1 [stats] In this demo, we will do some basic descriptive statistics.
Last week, we have used constant references to pass input arguments
into functions. We will now see how to use non-constant (mutable)
references to implement output and in/out arguments. The syntax for
a mutable reference is simply the type, the reference declarator (&) and
the name of the argument, i.e. dropping the const (compare data vs
PB161 Programming in C++ 11/114 June 28, 2022
median in the following function signature.
void stats( const std::vector< double > &data,
double &median, double &mean, double &stddev )
{
int n = data.size();
double sum = 0, square_error_sum = 0;
for ( double x_i : data )
sum += x_i;
Notice that we do not read the value of median before overwriting it
with the resulting value: this is a hallmark of an output argument – it
is never read before being written by the function.
mean = sum / n;
if ( n % 2 == 1 )
median = data[ n / 2 ];
else
median = ( data[ n / 2 ] + data[ n / 2 - 1 ] ) / 2;
However, after we have assigned a value to mean, we can continue to
use it like a normal read-write variable. It is important that the read
cannot be reached without executing the write first (e.g. it would be a
problem if the write above was conditional).
for ( double x_i : data )
square_error_sum += ( x_i - mean ) * ( x_i - mean );
double variance = square_error_sum / ( n - 1 );
stddev = std::sqrt( variance );
No return statement: the function was declared with void as its return
type, meaning that it does not return anything. The values are all
passed to the caller via output arguments.
}
int main() /* demo */
{
double median, mean, stddev;
std::vector< double > sample = { 2, 4, 4, 4, 5, 5, 5, 7, 9 };
stats( sample, median, mean, stddev );
assert( mean == 5 );
assert( median == 5 );
assert( stddev == 2 );
sample.push_back( 1100 );
stats( sample, median, mean, stddev );
assert( median == 5 );
assert( mean > 100 );
assert( stddev > 100 );
}
2.d.2 [primes] Besides simple output arguments, like in the previous
demo, we can pass values out of functions by manipulating existing
objects, most straightforwardly containers. In this demo, we will write
a function primes which appends prime numbers from a given range
to an existing std::vector. We will still call out an output argument,
though the concept is clearly more nuanced here. Like before, we will
use a mutable reference to achieve the desired semantics.
void primes( int from, int to, std::vector< int > &out )
{
for ( int candidate = from; candidate < to; ++ candidate )
{
bool prime = true;
int bound = std::sqrt( candidate ) + 1;
Decide whether a given number is prime, naively, by trial division.
for ( int div = 2; div < bound; ++ div )
if ( div != candidate && candidate % div == 0 )
{
prime = false;
break;
}
Now the interesting part: if the number was found to be prime, we
append it to the object referenced by out (i.e. the original object which
was declared outside this function and passed into it by reference).
Below in main, you can see that the content of the vector p_out changes
when we call this function on it.
if ( prime )
out.push_back( candidate );
}
}
int main() /* demo */
{
std::vector< int > p_out;
std::vector< int > p7 = { 2, 3, 5 },
p15 = { 2, 3, 5, 7, 11, 13 };
primes( 2, 7, p_out );
assert( p_out == p7 );
primes( 7, 15, p_out );
assert( p_out == p15 );
}
2.d.3 [iterate] In this short demo, we will introduce new syntax for
writing functions. The type of function we will use is called a lambda,
from the symbol that is used in lambda calculus to introduce anonymous
functions. In C++, lambdas are like regular functions with a few
extras.
Notice that iterate is declared as a variable – the function is on the
right-hand side, and does not have an intrinsic name (i.e. it is anonymous).
The type of iterate is not specified – instead, we have used auto,
to instruct the compiler to fill in the type.
Besides the missing name and the empty square brackets, the signature
of the lambda is similar to a standard function. However, on closer
inspection, another thing is missing: the return type. This might be
specified using -> type after the argument list, but if it is not, the compiler
will, again, deduce the type for us. The return type is commonly
omitted.
auto iterate = []( auto f, auto x, int count )
An advantage of a lambda is that we do not need to know the types of
all the arguments in advance: in particular, we don’t know the type
of f – this will most likely be a lambda itself (i.e. iterate is a higherorder
function). When this is the case, instead of the type, we specify
auto, instructing the compiler to deduce a type when the function is
used. This is the same principle which we have applied to the variable
iterate itself: we do not know the type, so we ask the compiler to fill it
in for us (by using auto). Let us continue by writing the body of iterate:
{
We want to build a vector of values, starting with x, then f(x), f(f(x)),
and so on. Immediately, we face a problem: what should be the type
of the vector? We need to specify the type parameter to declare the
variable, and this time we won’t be able to weasel out by just saying
auto, since the compiler can’t tell the type without an unambiguously
typed initializer. We have two options here:
1. in some circumstances, it is possible to omit the type parameter of
std::vector and let the compiler deduce only that. This would be
written std::vector out{ x } – by putting x into the vector right
from the start, the compiler can deduce that the element type
should be the same as the type of x, whatever that is; we will deal
PB161 Programming in C++ 12/114 June 28, 2022
with this mechanism much later in the course (in the last block); in
the meantime,
2. we can use decltype to obtain the type of x and use that to specify
the required type parameter for out, i.e.:
std::vector< decltype( x ) > out;
out.push_back( x );
We build the return vector by repeatedly calling f on the previous
value, until we hit count items.
for ( int i = 1; i < count; ++ i )
out.push_back( f( out.back() ) );
And we return the value, like in a regular function. Please also note
the semicolon after the closing brace: definition of a lambda is an expression,
and the variable declaration as a whole needs to be delimited
by a semicolon, just like in int x = 7;.
return out;
};
int main() /* demo */
{
auto f = []( int x ) { return x * x; };
auto g = []( int x ) { return x + 1; };
Of course, we can use auto in declaration of regular variables too, as
long as they are initialized.
auto v = iterate( f, 2, 4 );
std::vector< int > expect{ 2, 4, 16, 256 };
assert( v == expect );
std::vector< int >
iota = iterate( g, 1, 4 ),
iota_expect{ 1, 2, 3, 4 };
assert( iota == iota_expect );
}
2.d.4 [newton] This demonstration is as far as we’ll venture with regards
to numeric approximation – the exercises that deal with approximations
are all much simpler than this demo. Here, we will implement
the general Newton-Raphson method. This can be used for finding all
kinds of roots (zeroes of functions) numerically and for solving ‘hard’
(transcendental) equations.
The input to Newton’s method is a function f and its derivative, df.
A single improvement step then takes the current estimate x0 and
subtracts f(x)/df(x) from it. It is actually quite simple.
auto newton = []( auto f, auto df, double ini, double prec )
{
double x = ini, y = ini - f( x ) / df( x );
while ( std::fabs( y - x ) >= prec )
{
x = y;
y = y - f( x ) / df( x );
}
return y;
};
We can straightforwardly apply the above generic function to suitable
arguments to immediately implement some familiar functions, like
square roots or cube roots (we just need to find a function which becomes
zero if x is the square root of the argument of the function; that
function would be f(z) = z2
− x and its derivative is f′(z) = 2z).
double sqrt( double x, double prec ) /* square root */
{
return newton( [=]( double z ) { return z * z - x; },
[=]( double z ) { return 2 * z; }, 1, prec );
}
double cbrt( double n, double prec ) /* cube root */
{
return newton( [=]( double z ) { return z * z * z - n; },
[=]( double z ) { return 3 * z * z; }, 1, prec );
}
Compute nth root of x, generalizing sqrt and cbrt above.
double root( int n, double x, double prec )
{
auto f = [=]( double z ) { return std::pow( z, n ) - x; };
auto df = [=]( double z ) { return n * std::pow( z, n - 1 ); };
return newton( f, df, 1, prec );
}
Scroll to the end to see the test cases. The following code computes π
using only basic arithmetic and the Newton method… It’s all a bit fast
and loose, but it works. Enjoy.
Approximately evaluate a function using its truncated Taylor expan-
sion.
auto taylor = []( auto coeff, double x, double prec )
{
double r = 0, pow = 1, fact = 1;
int i = 0;
while ( pow / fact > prec / 10 )
{
r += coeff( i ) * pow / fact;
fact *= ++i;
pow *= x;
}
return r;
};
Shorthand for 4-periodic Taylor coefficients (like those that appear in
trigonometric functions).
auto trig_coeff( int a, int b, int c, int d )
{
return [=]( int i ) { return i % 4 == 0 ? a : i % 4 == 1 ? b :
i % 4 == 2 ? c : d; };
}
Sine and cosine, to feed into Newton.
double sine( double x, double prec )
{
return taylor( trig_coeff( 0, 1, 0, -1 ), x, prec );
}
double cosine( double x, double prec )
{
return taylor( trig_coeff( 1, 0, -1, 0 ), x, prec );
}
Compute π/2 as the root of cosine.
double pi( double prec )
{
auto f = [=]( double x ) { return cosine( x, prec ); };
auto df = [=]( double x ) { return -sine( x, prec ); };
return 2 * newton( f, df, 1, prec );
}
int main() /* demo */
{
for ( int decimals = 1; decimals < 10; ++ decimals )
PB161 Programming in C++ 13/114 June 28, 2022
{
double p = std::pow( 10, -decimals );
assert( std::fabs( sqrt( 2, p ) - std::sqrt( 2 ) ) < p );
assert( std::fabs( cbrt( 2, p ) - std::cbrt( 2 ) ) < p );
assert( std::fabs( root( 2, 2, p ) - std::sqrt( 2 ) ) < p );
assert( std::fabs( root( 3, 2, p ) - std::cbrt( 2 ) ) < p );
assert( std::fabs( root( 4, 16, p ) - 2 ) < p );
assert( std::fabs( pi( p ) - 4 * std::atan( 1 ) ) < p );
}
}
Part 2.e: Elementary Exercises
2.e.1 [fibonacci] Fill in an existing vector with a Fibonacci sequence
(i.e. after calling fibonacci( v, n ), the vector v should contain the
first n Fibonacci numbers, and nothing else).
// void fibonacci( … )
2.e.2 [normalize] Write a function to normalize a fraction, that is, find
the greatest common divisor of the numerator and denominator and
divide it out. Both numbers are given as in/out parameters.
// void normalize( … )
2.e.3 [accumulate] Write a function accumulate( f, vec ) which will
sum up f(x) for all x in the given std::vector< int > vec.
// auto accumulate = …
Part 2.p: Preparatory Exercises
2.p.1 [rewrap] A different take on word-wrapping. The idea is very
similar to last week – break lines at the first opportunity after you ran
out of space in your current line. The twist: do this by modifying the
input string. Additionally, undo existing line breaks if they are in the
wrong spot.
void rewrap( std::string &str, int cols );
2.p.2 [golden] The function next_fib should behave like this:
• given: a == fib( i ) and b == fib( i + 1 )
• execute: next_fib( a, b )
• to get: a == fib( i + 1 ) and b == fib( i + 2 ).
void next_fib( int &a, int &b );
Optional: Compute the n-th Fibonacci number using next_fib. Make
it so that: fib( 1 ) == 1, fib( 2 ) == 1, fib( 3 ) == 2. This is just to
practice working with next_fib in case you aren’t sure.
int fib( int n );
Approximate the golden ratio as the ratio of two consecutive Fibonacci
numbers. The precision argument gives an upper bound on the approximation
error. The number rounds is an output parameter and
gives us the number of iterations (calls to next_fib) that were required
to satisfy the precision requirement.
Notice that:
• the golden mean φ = 1.618...
• fib( 2 ) / fib( 1 ) = 1 / 1 = 1 is a lower bound
• fib( 3 ) / fib( 2 ) = 2 / 1 = 2 is an upper bound
• fib( 4 ) / fib( 3 ) = 3 / 2 = 1.5 is a lower bound
• fib( 5 ) / fib( 4 ) = 5 / 3 = 1.667 is an upper bound
and so on. Surely the error – distance from φ itself – in any given
round is smaller than its distance from the previous round.
double golden( double precision, int &rounds );
2.p.3 [divisors] Take a number, find all its prime divisors and add
them into divs, unless they are already there. Be sure to do this in time
proportional (linear) to the input number.
Bonus: If you assume that divs is sorted in ascending order when you
get it, you can make add_divisors a fair bit more efficient. Can you
figure out how?
void add_divisors( int num, std::vector< int > &divs );
2.p.4 [midpoints] A familiar class: add a 2-parameter constructor and
x(), y() accessors (the coordinates should be double-precision floating
point numbers).
class point;
Consider a closed shape made of line segments. Replace each segment
A with one that starts at the midpoint of A and ends at the midpoint
of B, the segment that comes immediately after A. The input is given
as a sequence of points (each point shared by two segments). The last
segment goes from the last point to the first point (closing the shape).
void midpoints( std::vector< point > &pts );
helper functions for floating-point almost-equality
bool near( double a, double b )
{
return std::fabs( a - b ) < 1e-8;
}
bool near( point a, point b )
{
return near( a.x(), b.x() ) && near( a.y(), b.y() );
}
2.p.5 [higher] Write a map function, which takes a function f and a
vector v and returns a new vector w such that w[ i ] = f( v[ i ] ) for any
valid index i. We will need to use the ‘lambda’ syntax for this, since
we don’t yet know any other way to write functions which accept
functions as arguments.
// static auto map = []( ... ) { ... };
Similar, but f is a binary function, and there are two input vectors of
equal length. You do not need to check this.
// static auto zip = []( ... ) { ... };
You can assume that the output vector is of the same type as the input
vector (i.e. f is of type a → a in map, and of type a → b → a for zip.
2.p.6 [fixpoint] A fixed point of a function f is an x such that f(x) = x.
A function is monotonic if ∀x, y.x ≤ y → f(x) ≤ f(y). Assume that f
is a monotonic function and hence, since there are only finitely many
int values, that it has at least one fixed point. Find the greatest fixed
point of f.
// auto fixpoint = …
int f( int x ) { return x / 2; }
int g( int x ) { return x - x / 20; }
int h( int x ) { return std::max( x / 5, 20 ); }
int i( int x ) { return x < INT_MAX ? x + 1 : x; }
PB161 Programming in C++ 14/114 June 28, 2022
Part 2.r: Regular Exercises
2.r.1 [euler] This is a straightforward math exercise. Implement
Euler’s [φ], for instance using the product formula φ(n) = nΠ(1 − 1/p)
where the product is over all distinct prime divisors of n. You may
need to take care to compute the result exactly.
long phi( long n ); /* ref: 21 lines */
2.r.2 [approx] Remember fib.cpp? We can do a bit better. Let’s decompose
our golden() function differently this time.
The approx function is a higher-order one. What it does is it calls f()
repeatedly to improve the current estimate, until the estimates are
sufficiently close to each other (closer than the given precision). The
init argument is our initial estimate of the result.
// auto approx = []( auto f, double init, double prec ) { ... };
Use approx to compute the golden mean. Note that you don’t need
to use the previous estimate in your improvement function. Use byreference
captures to keep state between iterations if you need some.
double golden( double prec );
The Babylonian (Heron) method to compute square roots. Please take
note, you may find it helpful later. This is how approx is supposed to be
used.
double sqrt( double n, double prec )
{
auto improve = [=]( double last )
{
double next = n / last;
return ( last + next ) / 2;
};
return approx( improve, 1, prec );
}
2.r.3 [solve] Consider a single-player game that takes place on a 1D
playing field like this:
0…2……42
The player starts at the leftmost cell and in each round can decide
whether to jump left or right. The playing field is given by the input
vector jumps. The size of the field is jumps.size() + 1 (the rightmost
cell is always 0). The objective is to visit each cell exactly once.
bool solve( std::vector< int > jumps );
2.r.4 [sort] Implement an in-place selection sort of a vector of integers,
using a comparator passed to the sort routine as an argument. A
comparator is a function that is used to compare elements instead of
the builtin relational operators. This is useful if your data is sorted in
non-standard manner.
// auto selectsort = []( std::vector< int > &to_sort, auto cmp ) …;
2.r.5 [permute] Given a number n and a base b, find all numbers whose
digits (in base b) are a permutation of the digits of n and return them
as a vector of integers. Each such number should appear exactly once.
Examples:
(125)₁₀ → { 125, 152, 215, 251, 512, 521 }
(1f1)₁₆ → { (1f1)₁₆, (f11)₁₆, (11f)₁₆ }
(20)₁₀ → { 20, 2 }
std::vector< unsigned > permute_digits( unsigned n, int base );
std::vector< unsigned > to_digits( unsigned n, int base, int fill =
0 )
{
std::vector< unsigned > ds;
while ( n > 0 || fill > 0 )
{
ds.push_back( n % base );
n /= base;
-- fill;
}
return ds;
}
void check( unsigned n, int base,
const std::vector< unsigned > &expect )
{
auto got = permute_digits( n, base );
std::set< unsigned > uniq( got.begin(), got.end() );
assert( got.size() == expect.size() );
assert( got.size() == uniq.size() );
auto n_digits = to_digits( n, base );
std::sort( n_digits.begin(), n_digits.end() );
for ( unsigned p : got )
{
auto p_digits = to_digits( p, base, n_digits.size() );
std::sort( p_digits.begin(), p_digits.end() );
assert( n_digits == p_digits );
}
}
2.r.6 [bsearch] Implement binary search on a vector, with a twist: the
order of the elements is given by a comparator. This is a function that
is passed as an argument to search and is used to compare elements
instead of the builtin relational operators. This is useful if your data is
sorted in non-standard manner.
// auto search = []( std::vector< int > &vec, int val, auto cmp );
Part 3: Containers
This week will be about containers (collections).
Demonstrations:
1. freq – a word frequency histogram
2. dfs – reachability using recursive depth-first search
3. closure – closure properties of relations
4. bfs – find the nearest matching node
Elementary exercises:
1. unique – remove duplicated entries from a vector
2. reflexive – compute a reflexive closure of a relation
3. normalize – scale an input vector into a 0-1 range
Preparatory exercises:
1. brackets – check that brackets in a string balance out
PB161 Programming in C++ 15/114 June 28, 2022
2. connected – decompose a graph into connected components
3. dag – check whether a graph is acyclic (dfs again)
4. rel – a tiny bit of relational algebra
5. numbers – a slightly enriched set of numbers
6. bipartite – bipartiteness checking using BFS
Regular exercises:
1. mode – find the mode (most common value) in a vector
2. buckets – sort items into buckets based on an attribute
3. shortest – shortest distances in an unweighted graph
4. flood – flood fill in a grid
5. colour – brute-force a 3-colouring of a graph
6. life – the game of life
Part 3.d: Demonstrations
3.d.1 [freq] In this demo, we will build up a histogram of word appearances.
Since we will want to process the input incrementally, we will
implement the word counter as a class with 2 methods: process, which
will add each word that appears in its argument to the histogram, and
count, which takes a single-word string as an argument and returns
how many times it has been encountered by process.
class freq
{
All the heavy lifting will be done by the standard associative container,
std::map. We will use std::string as the key type (holding the word of
interest) and int as the value type: the number of appearances of this
word.
std::map< std::string, int > _counter;
public:
We will first implement a helper method, for counting a single word.
It will be convenient to ignore empty strings here, so we will do just
that. Notice that we use the indexing (subscript) operator to access the
value which std::map associates with the given key. Also notice that
the key is automatically added to the map in case it is not yet present.
void add( const std::string &word )
{
if ( !word.empty() )
_counter[ word ] ++;
}
Now the main workhorse: process takes an input string, decomposes it
into individual words and counts them. Notice the use of += to append
a letter to an existing string.
void process( const std::string &str )
{
std::string word;
for ( auto c : str )
if ( std::isblank( c ) )
{
add( word );
word.clear();
}
else
word += c;
Do not forget to add the last word, in case it was not followed by a
blank.
add( word );
}
We would clearly like to mark the count method, which simply returns
information about the observed frequency of a word, as const. However,
the subscript operator on an std::map is not const – this is because,
as we have mentioned earlier, should the key not be present in the
map, it will be added automatically, thus changing the content of the
container.
Instead, we can ask std::map to check whether the key is present (by
using count), without adding it. If the key is missing, we simply return
0. Otherwise, we ask the map to find the value associated with the
key, again without adding it if it is missing. Note that dereferencing
the result of find is undefined if the key is not present (in this case, we
know for sure that the key is present – we just checked). All std::map
methods which we used are marked const and hence we can mark our
count method const as well, as we desired.
int count( const std::string &s ) const
{
return _counter.count( s ) ? _counter.find( s )->second : 0;
}
};
int main() /* demo */
{
freq f;
We create a const alias for f, so that we check that it is indeed possible
to call count on it.
const freq &cf = f;
assert( cf.count( "hello" ) == 0 );
assert( cf.count( "" ) == 0 );
f.process( "hello world" );
assert( cf.count( "hello" ) == 1 );
assert( cf.count( "hell" ) == 0 );
assert( cf.count( "world" ) == 1 );
assert( cf.count( " world" ) == 0 );
f.process( "hello hello" );
assert( cf.count( "hello" ) == 3 );
assert( cf.count( "world" ) == 1 );
f.process( "world hello world hello world" );
assert( cf.count( "hello" ) == 5 );
assert( cf.count( "world" ) == 4 );
}
3.d.2 [dfs] In this demo, we will do some basic exploration of directed
graphs. Probably the simplest possible algorithm for that is recursive
depth-first search, so that is what we will use. We will be interested
in the question ‘is vertex a reachable from vertex b?’.
The input graph is given using adjacency lists: the graph type gives the
successors for each vertex present in the graph. Please note that in principle,
the set of vertices does not need to be contiguous, or composed
of only small numbers (hence the std::map and not an std::vector).
using edges = std::vector< int >;
using graph = std::map< int, edges >;
Besides the graph itself, we will need to represent the visited set – the
set of vertices that have already been visited by the algorithm. In a
graph with loops, not keeping track of this information would lead to
infinite recursion. In an acyclic graph, it could still lead to exponential
running time. Since in pseudocode, this is a literal set, using std::set
sounds like a good idea. Indeed, std::set is a container which keeps
at most one copy of any element, and provides efficient (logarithmic
time) lookup and insertion.
using visited = std::set< int >;
PB161 Programming in C++ 16/114 June 28, 2022
The main recursive function needs 2 auxiliary arguments: the set
of already-visited vertices seen and the boolean moved, which guards
against the case when we ask whether a vertex is reachable from itself
– this is traditionally only answered in affirmative when there is a path
from that vertex to itself, but a naive solution would always answer
true. Hence, we need to ensure at least one edge was traversed before
returning true. The question this function answers is ‘is there a path
which starts in vertex from, does not visit any of the vertices in seen
and ends in to?’
Notice that seen is passed around by reference: there is only a single
instance of this set, shared by all recursive calls. That is, if one
branch of the search visits a vertex, it will also be avoided by any subsequent
sibling branches (not just by the recursive calls made within
the branch).
bool is_reachable_rec( const graph &g, int from, int to,
visited &seen, bool moved )
{
The base case of the recursion is when we reach the target vertex and
have already traversed at least one edge. In this case, we return true:
we have found a path connecting the two vertices.
if ( from == to && moved )
return true;
The main loop looks at each successor of from and calls is_reachable
recursively, asking whether there is a path from the successor to the
goal state, avoiding the current state. The result of the g.at call is
a (reference to) the edges container (i.e. the std::vector of vertices).
Hence next ranges over the successors of the vertex from.
for ( auto next : g.at( from ) )
In case next was not yet seen (it is not present in the visited set), mark
it as visited and proceed to explore it recursively.
if ( !seen.count( next ) )
{
seen.insert( next );
if ( is_reachable_rec( g, next, to, seen, true ) )
return true;
}
We have failed to find a satisfactory path, having exhausted all the
options. Return false.
return false;
}
Finally, we provide a simple wrapper around the recursive function
above, providing initial values for the two auxiliary arguments. Check
whether to can be reached by following one or more edges if we start
at from.
bool is_reachable( const graph &g, int from, int to )
{
visited seen;
return is_reachable_rec( g, from, to, seen, false );
}
int main() /* demo */
{
graph g{ { 1, { 2, 3, 4 } },
{ 2, { 1, 2 } },
{ 3, { 3, 4 } },
{ 4, {} },
{ 5, { 3 }} };
assert( is_reachable( g, 1, 1 ) );
assert( !is_reachable( g, 4, 4 ) );
assert( is_reachable( g, 1, 2 ) );
assert( is_reachable( g, 1, 3 ) );
assert( is_reachable( g, 1, 4 ) );
assert( !is_reachable( g, 4, 1 ) );
assert( is_reachable( g, 3, 3 ) );
assert( !is_reachable( g, 3, 1 ) );
assert( is_reachable( g, 5, 4 ) );
assert( !is_reachable( g, 5, 1 ) );
assert( !is_reachable( g, 5, 2 ) );
}
3.d.3 [closure] In this demo, we will check closure properties of relations:
reflexivity, transitivity and symmetry. A relation is a set of pairs,
and hence we will represent them as std::set of std::pair instances.
We will work with relations on integers. Recall that std::set has an
efficient membership test: we will be using that a lot in this program.
using relation = std::set< std::pair< int, int > >;
The first predicate checks reflexivity: for any x which appears in the relation,
the pair (x, x) must be present. Besides membership testing, we
will use structured bindings and range for loops. Notice that a braced
list of values is implicitly converted to the correct type (std::pair< int,
int >).
bool is_reflexive( const relation &r )
{
Structured bindings are written using auto, followed by square brackets
with a list of names to bind to individual components of the right-hand
side. In this case, the right-hand side is the loop variable – i.e. each of
the elements of r in turn.
for ( auto [ x, y ] : r )
{
if ( !r.count( { x, x } ) )
return false;
if ( !r.count( { y, y } ) )
return false;
}
We have checked all the elements of r and did not find any which
would violate the required property. Return true.
return true;
}
Another, even simpler, check is for symmetry. A relation is symmetric
if for any pair (x, y) it also contains the opposite, (y, x).
bool is_symmetric( const relation &r )
{
for ( auto [ x, y ] : r )
if ( !r.count( { y, x } ) )
return false;
return true;
}
Finally, a slightly more involved example: transitivity. A relation is
transitive if ∀x, y, z.(x, y) ∈ r ∧ (y, z) ∈ r → (x, z) ∈ r.
bool is_transitive( const relation &r )
{
for ( auto [ x, y ] : r )
for ( auto [ y_prime, z ] : r )
if ( y == y_prime && !r.count( { x, z } ) )
return false;
return true;
}
int main() /* demo */
{
relation r_1{ { 1, 1 }, { 1, 2 } };
PB161 Programming in C++ 17/114 June 28, 2022
assert( !is_reflexive( r_1 ) );
assert( !is_symmetric( r_1 ) );
assert( is_transitive( r_1 ) );
relation r_2{ { 1, 1 }, { 1, 2 }, { 2, 2 } };
assert( is_reflexive( r_2 ) );
assert( !is_symmetric( r_2 ) );
assert( is_transitive( r_2 ) );
relation r_3{ { 2, 1 }, { 1, 2 }, { 2, 2 } };
assert( !is_reflexive( r_3 ) );
assert( is_symmetric( r_3 ) );
assert( !is_transitive( r_3 ) );
}
3.d.4 [bfs] The goal of this demonstration will be to find the shortest
distance in an unweighted, directed graph:
1. starting from a fixed (given) vertex,
2. to the nearest vertex with an odd value.
The canonical ‘shortest path’ algorithm in this setting is breadth-first
search. The algorithm makes use of two data structures: a queue and a
set, which we will represent using the standard C++ containers named,
appropriately, std::queue5
and std::set.
In the previous demonstration, we have represented the graph explicitly
using adjacency list encoded as instances of std::vector. Here, we
will take a slightly different approach: we well use std::multimap – as
the name suggests, it is related to std::map with one crucial difference:
it can associate multiple values to each key. Which is exactly what we
need to represent an directed graph – the values associated with each
key will be the successors of the vertex given by the key.
using graph = std::multimap< int, int >;
The algorithm consists of a single function, distance_to_odd, which
takes the graph g, as a constant reference, and the vertex initial, as
arguments. It then returns the sought distance, or if no matching
vertex is found, -1.
int distance_to_odd( const graph &g, int initial )
{
We start by declaring the visited set, which prevents the algorithm
from getting stuck in an infinite loop, should it encounter a cycle in the
input graph (and also helps to keep the time complexity under control).
std::set< int > visited;
The next piece of the algorithm is the exploration queue: we will put
two pieces of information into the queue: first, the vertex to be explored,
second, its BFS distance from initial.
std::queue< std::pair< int, int > > queue;
To kickstart the exploration, we place the initial vertex, along with
distance 0, into the queue:
queue.emplace( initial, 0 );
Follows the standard BFS loop:
while ( !queue.empty() )
{
auto [ vertex, distance ] = queue.front();
queue.pop();
5
Strictly speaking, std::queue is not a container, but rather a container adaptor. Internally, unless
specified otherwise, an std::queue uses another container, std::deque to store the data and
implement the operations. It would also be possible, though less convenient, to use std::deque
directly.
To iterate all the successors of a vertex in an std::multimap, we will
use its equal_range method, which will return a pair of iterators – generalized
pointers, which support a kind of ‘pointer arithmetic’. The
important part is that an iterator can be incremented using the ++
operator to get the next element in a sequence, and dereferenced using
the unary * operator to get the pointed-to element. The result of
equal_range is a pair of iterators:
• begin, which points at the first matching key-value pair in the mul-
timap,
• end, which points one past the last matching element; clearly, if
begin == end, the sequence is empty.
Incrementing begin will eventually cause it to become equal to end, at
which point we have reached the end of the sequence. Let’s try:
auto [ begin, end ] = g.equal_range( vertex );
for ( ; begin != end; ++ begin )
{
In the body loop, begin points, in turn, at each matching key-value pair
in the graph. To get the corresponding value (which is what we care
about), we extract the second element:
auto [ _, next ] = *begin;
if ( visited.count( next ) )
continue; /* skip already-visited vertices */
First, let us check whether we have found the vertex we were looking
for:
if ( next % 2 == 1 )
return distance + 1;
Otherwise we mark the vertex as visited and put it into the queue,
continuing the search.
visited.insert( next );
queue.emplace( next, distance + 1 );
}
}
We have exhausted the queue, and hence all the vertices reachable
from initial, without finding an odd-valued one. Indicate failure to
the caller.
return -1;
}
int main() /* demo */
{
graph g{ { 1, 2 }, { 1, 6 }, { 2, 4 }, { 2, 5 }, { 6, 4 } },
h{ { 8, 2 }, { 8, 6 }, { 2, 4 }, { 2, 5 }, { 5, 8 } },
i{ { 2, 4 }, { 4, 2 } };
assert( distance_to_odd( g, 1 ) == 2 );
assert( distance_to_odd( g, 2 ) == 1 );
assert( distance_to_odd( g, 6 ) == -1 );
assert( distance_to_odd( h, 8 ) == 2 );
assert( distance_to_odd( h, 5 ) == 3 );
assert( distance_to_odd( i, 2 ) == -1 );
}
Part 3.e: Elementary Exercises
3.e.1 [unique] Filter out duplicate entries from a vector, maintaining
the relative order of entries. Return the result as a new vector.
std::vector< int > unique( const std::vector< int > & );
PB161 Programming in C++ 18/114 June 28, 2022
3.e.2 [reflexive] Build a reflexive closure of a relation given as a set
of pairs, returning the result.
using relation = std::set< std::pair< int, int > >;
relation reflexive( const relation &r );
3.e.3 [normalize] Given a vector of non-negative floating-point numbers,
produce a new vector where all entries fall into the 0-1 range,
and they are all related to the original entries by the same factor.
using signal_t = std::vector< double >;
signal_t normalize( const signal_t & );
Part 3.p: Preparatory Exercises
3.p.1 [brackets] Check that curly and square brackets in a given string
balance out correctly.
bool balanced( const std::string & );
3.p.2 [connected] Decompose an undirected graph into connected components
(described by a set of sets of numbers). The graph is given
as a symmetric adjacency matrix. Vertices are numbered from 1 to n
where n is the dimension of the input matrix.
using graph = std::vector< std::vector< bool > >;
using component = std::set< int >;
using components = std::set< component >;
components decompose( const graph &g );
3.p.3 [dag] Another exercise for graph exploration, this time we will
look for cycles. There are a few algorithms to choose from, those based
on DFS are probably the most straightforward.
This time, the input graph is given as a multimap: a map which can
contain multiple values for each key. In other words, it behaves as a
set of pairs with additional support for efficient retrieval based on the
value of the first field of the pair. The is_dag function should return
false iff g contains a cycle. The graph does not need to be connected.
using graph = std::multimap< int, int >;
bool is_dag( const graph &g );
3.p.4 [rel] This exercise demonstrates use of std::tuple and structured
bindings. Since we cannot write generic code yet (and even if
we did, writing the below operators in full generality would be rather
tricky), we will only work with a fixed set of types (relations).
First a bunch of type aliases: item and its variants each represent a
single row, while rel and its variants represent an entire relation.
using item = std::tuple< std::string, int, double >;
using item_dbl = std::tuple< std::string, double >;
using item_int = std::tuple< std::string, int >;
using rel = std::set< item >;
using rel_dbl = std::set< item_dbl >;
using rel_int = std::set< item_int >;
Projections: keep a subset of columns, in this case the string and either
of the numeric columns.
rel_int project_int( const rel & );
rel_dbl project_dbl( const rel & );
Selection: keep a subset of rows – those that match on the given column.
Throw away all the rest.
rel select_str( const rel &, const std::string &n );
rel select_int( const rel &, int n );
3.p.5 [numbers] The class represents a set of integers; operations:
• add – adds a number, returns true if it was new
• del – removes a number, returns true if it was present
• del_range – removes numbers within given bounds (inclusive)
• merge – adds all numbers from another instance
• has – returns true if the given number is in the set
Complexity requirements:
• del_range and merge must run in O(n) time
• everything else in O(logn) time
class numbers;
3.p.6 [bipartite]
using edges = std::vector< int >;
using graph = std::map< int, edges >;
Check whether a given graph is bipartite. The graph is undirected, i.e.
its adjacency relation is symmetric.
bool is_bipartite( const graph &g );
Part 3.r: Regular Exercises
3.r.1 [mode] Find the mode (most common value) in a non-empty vector
and return it. If there are more than one, return the smallest.
int mode( const std::vector< int > & );
3.r.2 [buckets] Sort stones into buckets, where each bucket covers a
range of weights; the range of stone weights to put in each bucket is
given in an argument – a vector with one element per bucket, each element
a pair of min/max values (inclusive). Assume the bucket ranges
do not overlap. Stones are given as a vector of weights. Throw away
stones which do not fall into any bucket. Return the weights of individual
buckets.
using bucket = std::pair< int, int >;
std::vector< int > sort( const std::vector< int > &stones,
const std::vector< bucket > &buckets );
3.r.3 [shortest] Compute single-source shortest path distances for all
vertices in an unweighted directed graph. The graph is given using
adjacency (successor) lists. The result is a map from a vertex to its
shortest distance from initial. Vertices which are not reachable from
initial should not appear in the result.
using edges = std::vector< int >;
using graph = std::map< int, edges >;
std::map< int, int > shortest( const graph &g, int initial );
3.r.4 [flood] In this exercise, we will implement a simple flood fill: in
its most common formulation, this is an algorithm which:
1. is given a bitmap (a rectangular grid of pixels),
2. a starting position in the grid,
3. a fill colour,
and changes the entire contiguous single-colour area that contains the
starting position to use the fill colour.
We will do a monochromatic version of the same (pixels are either
white or black, or rather 0 or 1) and instead of modifying the input
grid, or building a new one, we will simply count how many cells
change colour. Example (the starting position was 1, 3):
0 1 2 3 4 5 6 0 1 2 3 4 5 6
PB161 Programming in C++ 19/114 June 28, 2022
0 0 0 0 1 0 0 0 1 1 1 1 0 0 0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
2
3
4
5
Notice that the flood also proceeds along diagonals (i.e. from position
(2, 3) to (3, 4) and then further to (4, 3)). The grid is given as a single,
flat vector and a width. You can assume that the size of the vector
is evenly divisible by the given width. The x0 and y0 give the starting
position, while the last argument, fill, the colour (0 or 1) to use.
using grid = std::vector< bool >;
int flood( const grid &pixels, int width,
int x0, int y0, bool fill );
3.r.5 [colour] Write a function to decide whether a given graph can be
3-colored. A correct colouring is an assignment of colours to vertices
such that no edge connects vertices with the same colour. The graph
is given as a set of edges. Edges are represented as pairs; assume that
if (u, v) is a part of the graph, so is (v, u).
using graph = std::set< std::pair< int, int > >;
bool has_3colouring( const graph &g );
3.r.6 [life] The game of life is a 2D cellular automaton: cells form a
2D grid, where each cell is either alive or dead. In each generation
(step of the simulation), the new value of a given cell is computed from
its value and the values of its 8 neighbours in the previous generation.
The rules are as follows:
state alive neigh. result
alive 0–1 dead
alive 2–3 alive
alive 4–8 dead
dead 0–2 dead
dead 3 alive
dead 4-8 dead
An example of a short periodic game:
○○○
○
○
○
○○○→ →
Write a function which, given a set of live cells, computes the set of live
cells after n generations. Live cells are given using their coordinates in
the grid, i.e. as (x, y) pairs.
using cell = std::pair< int, int >;
using grid = std::set< cell >;
grid life( const grid &, int );
Part 4: Overloading, Constructors and Lifetime
First, we will look at function and method overloading, including overloading
of constructors and overloading on reference kinds. We will
also touch the topic of object lifetime (which considers the question
of when exactly is an object valid and can be used) and ownership
(controlling the lifetime of ‘subordinate’ objects, e.g. elements in a
container).
Demonstrations:
1. art – overloading basics, with books and paintings
2. numbers – a list of numbers which remember their type
3. refs – overloading with references
4. pool – ownership and indirect references
Elementary exercises:
1. diameter – basic function overloading (circle diameter)
2. circle – same story, but with constructors
3. index – access elements of different types using indices
Preparatory exercises:
1. format – method overloading 101
2. least – return a least element without making copies
3. area – geometry with function and ctor overloads
4. zipper – const method overloading on a zipper
5. rpn – postfix arithmetic with more overloading
6. eval – infix evaluation with a node pool
Regular exercises:
1. complex – complex numbers and function overloading
2. bsearch – binary search versus const
3. search – binary search tree with a pool of nodes
4. bitptr – pointer to a single bit
5. readint – read integers from various string types
6. sort – choosing a sorting algorithm
Part 4.d: Demonstrations
4.d.1 [art] In this demo, we will look at overloading of standard
toplevel functions. We will use 3 record types to represent artistic
works: books of fiction, musical compositions and paintings. They
have some common attributes, but they are also quite different. We
will use function overloading to provide uniform access to the common
attributes.
We will use a very simplified view of periodization of art, one that can
be more-or-less applied to all 3 types of work which we are interested
in. It’s perhaps important to note, that the historical periods associated
with those styles do not exactly coincide in the 3 disciplines.
enum class style_t
{
antique, medieval, renaissance, baroque, classical, romantic,
modern
};
The three record types: a book has an author, a name and a publisher,
along with a style. A composition additionally has a key (e.g. ‘c minor’)
and a list of parts. On the other hand, a painting does not have a
publisher, but we can associate a technique with it (say, ‘oil on canvas’).
For simplicity, we store everything as free-form strings .
struct book
{
std::string author, name, publisher;
style_t style;
};
struct composition
PB161 Programming in C++ 20/114 June 28, 2022
{
std::string author, name, key, publisher;
std::vector< std::string > parts;
style_t style;
};
struct painting
{
std::string author, name, technique;
style_t style;
};
Now the functions: the first will be the simplest, essentially just forwarding
to attribute access. In practice, a function like this is not
especially useful, but it is simple.
std::string author( book b ) { return b.author; }
std::string author( composition c ) { return c.author; }
std::string author( painting p ) { return p.author; }
A slightly more interesting function will be description, which takes
some of the attributes and combines them into a single humanreadable
string describing the work.
std::string description( book b )
{
return b.name + " by " + b.author;
}
std::string description( composition c )
{
return c.name + " in " + c.key + " by " + c.author;
}
std::string description( painting p )
{
return p.name + " by " + p.author + " (" + p.technique + ")";
}
Another attribute that is shared by books and composition is the name
of the publisher. But there is no equivalent concept for paintings. What
now? There are a few options: we could leave the overload undefined,
which is clearly correct, but not super helpful. Or we can implement
an overload which returns some placeholder value. Let’s do that here.
std::string publisher( book b ) { return b.publisher; }
std::string publisher( composition c ) { return c.publisher; }
std::string publisher( painting ) { return "n/a"; }
And finally, for the thorny issue of periods. We sort-of managed to
come up with a list of periods which we can sort-of apply to everything,
but the years covered differ in each discipline. So the overloads will
take care of this.
std::pair< int, int > period( book b )
{
switch ( b.style )
{
case style_t::antique: return { -1200, 455 };
case style_t::medieval: return { 455, 1485 };
case style_t::renaissance: return { 1485, 1660 };
case style_t::baroque: return { 1600, 1680 };
case style_t::classical: return { 1660, 1790 };
case style_t::romantic: return { 1770, 1850 };
case style_t::modern: return { 1850, 2021 };
default: assert( false );
}
}
std::pair< int, int > period( composition c )
{
switch ( c.style )
{
case style_t::antique: return { -1300, 500 };
case style_t::medieval: return { 500, 1400 };
case style_t::renaissance: return { 1400, 1600 };
case style_t::baroque: return { 1580, 1750 };
case style_t::classical: return { 1750, 1820 };
case style_t::romantic: return { 1800, 1910 };
case style_t::modern: return { 1890, 2021 };
default: assert( false );
}
}
std::pair< int, int > period( painting p )
{
switch ( p.style )
{
case style_t::antique: return { -3000, 500 };
case style_t::medieval: return { 500, 1400 };
case style_t::renaissance: return { 1300, 1600 };
case style_t::baroque: return { 1600, 1730 };
case style_t::classical: return { 1780, 1850 };
case style_t::romantic: return { 1800, 1860 };
case style_t::modern: return { 1860, 2021 };
default: assert( false );
}
}
Finally, we will check that we can indeed call the functions uniformly
on different types input types.
int main() /* demo */
{
book antigone{ "Sophocles", "Antigone", "n/a", style_t::antique
},
miserables{ "Victor Hugo", "Les Misérables",
"A. Lacroix, Verboeckhoven & Cie.",
style_t::romantic };
composition
bach_mass{ "J. S. Bach", "Mass", "b minor",
"Bach Gesellshaft",
{ "soprano 1", "soprano 2", "alto", "tenor",
"bass", "flute 1", "flute 2", "oboe/d'amore 1",
"oboe/d'amore 2", "oboe 3", "bassoon 1",
"bassoon 2", "horn", "trumpet 1", "trumpet 2",
"trumpet 3", "timpani", "violin 1", "violin 2",
"viola", "basso continuo" },
style_t::baroque },
fantasia{ "Bohuslav Martinů", "Fantasia H.301", "n/a",
"Max Eschig",
{ "theremin", "oboe",
"violin 1", "violin 2", "viola", "violoncello",
"piano" },
style_t::modern };
painting babel{ "Pieter Bruegel the Elder",
"The Tower of Babel",
"oil on wood", style_t::renaissance },
boon{ "James Brooks", "Boon", "oil on canvas",
style_t::modern };
Getting a description:
assert( description( bach_mass ) ==
"Mass in b minor by J. S. Bach" );
assert( description( babel ) ==
"The Tower of Babel by Pieter Bruegel the Elder "
"(oil on wood)" );
assert( description( antigone ) == "Antigone by Sophocles" );
And periods:
assert( period( bach_mass ) == std::pair( 1580, 1750 ) );
PB161 Programming in C++ 21/114 June 28, 2022
assert( period( fantasia ) == std::pair( 1890, 2021 ) );
assert( period( boon ) == std::pair( 1860, 2021 ) );
}
4.d.2 [numbers] In this demonstration, we will look at overloading: both
of regular methods and of constructors. The first class which we will
implement is number, which can represent either a real (floating-point)
number or an integer. Besides the attributes integer and real which
store the respective numbers, the class remembers which type of number
it stores, using a boolean attribute called is_real.
struct number
{
bool is_real;
int integer;
double real;
We provide two constructors for number: one for each type of number
that we wish to store. The overload is selected based on the type of
argument that is provided.
explicit number( int i ) : is_real( false ), integer( i ) {}
explicit number( double r ) : is_real( true ), real( r ) {}
};
The second class will be a container of numbers which directly allows
the user to insert both floating-point and integer numbers, without
converting them to a common type. To make insertion convenient,
we provide overloads of the add method. Access to the numbers is
index-based and is provided by the at method, which is overloaded for
entirely different reasons.
class numbers
{
The sole attribute of the numbers class is the backing store, which is an
std::vector of number instances.
std::vector< number > _data;
public:
The two add overloads both construct an appropriate instance of number
and push it to the backing vector. Nothing surprising there.
void add( double d ) { _data.emplace_back( d ); }
void add( int i ) { _data.emplace_back( i ); }
The overloads for at are much more subtle: notice that the argument
types are all identical – there are only 2 differences, first is the return
type, which however does not participate in overload resolution. If
two functions only differ in return type, this is an error, since there is
no way to select which overload should be used.
The other difference is the const qualifier, which indeed does participate
in overload resolution. This is because methods have a hidden
argument, this, and the trailing const concerns this argument. The
const method is selected when the call is performed on a const object
(most often because the call is done on a constant reference).
const number &at( int i ) const { return _data.at( i ); }
number &at( int i ) { return _data.at( i ); }
};
int main() /* demo */
{
numbers n;
n.add( 7 );
n.add( 3.14 );
assert( !n.at( 0 ).is_real );
assert( n.at( 1 ).is_real );
assert( n.at( 0 ).integer == 7 );
Notice that it is possible to assign through the at method, if the object
itself is mutable. In this case, overload resolution selects the second
overload, which returns a mutable reference to the number instance
stored in the container.
n.at( 0 ) = number( 3 );
assert( n.at( 0 ).integer == 3 );
However, it is still possible to use at on a constant object – in this
case, the resolution picks the first overload, which returns a constant
reference to the relevant number instance. Hence, we cannot change
the number this way (as we expect, since the entire object is constant,
and hence also each of its components).
const numbers &n_const = n;
assert( n_const.at( 0 ).integer == 3 );
// n_const.at( 1 ) = number( 1 ); this will not compile
}
4.d.3 [refs] In this demonstration, we will look at overloading functions
based on different kinds of references. This will allow us to adapt
our functions to the kind of value (and its lifetime) that is passed to
them, and to deal with arguments efficiently (without making unnecessary
copies). But first, let’s define a few type aliases:
using int_pair = std::pair< int, int >;
using int_vector = std::vector< int >;
using int_matrix = std::vector< int_vector >;
Our goal will be simple enough: write a function which gives access to
the first element of any of the above types. In the case of int_matrix,
the element is an entire row, which has some important implications
that we will discuss shortly.
Our main requirements will be that:
1. first should work correctly when we call it on a constant,
2. when called on a mutable value, first( x ) = y should work and
alter the value x (i.e. update the first element of x).
These requirements are seemingly contradictory: if we return a value
(or a constant reference), we can satisfy point 1, but we fail point 2.
If we return a mutable reference, point 2 will work, but point 1 will
fail. Hence we need the result type to be different depending on the
argument. This can be achieved by overloading on the argument type.
However, we still have one problem: how do we tell apart, using a type,
whether the passed value was constant or not? Think about this: if
you write a function which accepts a mutable reference, it cannot be
called on an argument which is constant: the compiler will complain
about the value losing its const qualifier (if you never encountered this
behaviour, try it out; it’s important that you understand this).
But that means that first( int_pair &arg ) can only be called on mutable
arguments, which is exactly what we need. Fortunately for us, if
the compiler decides that this particular first cannot be used (because
of missing const), it will keep looking for some other first that might
work. You hopefully remember that first( const int_pair &arg ) can
be called on any value of type int_pair (without creating a copy). If we
provide both, the compiler will use the non-const version if it can, but
fall back to the const one otherwise. And since overloaded functions
can differ in their return type, we have our solution:
int &first( int_pair &p ) { return p.first; }
int first( const int_pair &p ) { return p.first; }
The case of int_vector is completely analogous:
int &first( int_vector &v ) { return v[ 0 ]; }
int first( const int_vector &v ) { return v[ 0 ]; }
Since in the above cases, the return value was of type int, we did
not bother with returning const references. But when we look at
PB161 Programming in C++ 22/114 June 28, 2022
int_matrix, the situation has changed: the value which we return is an
std::vector, which could be very expensive to copy. So we will want
to avoid that. The first case (mutable argument), stays the same – we
already returned a reference in this case.
int_vector &first( int_matrix &v ) { return v[ 0 ]; }
At first glance, the second case would seem straightforward enough
– just return a const int_vector & and be done with it. But there is
a catch: what if the argument is a temporary value, which will be
destroyed at the end of the current statement? It’s not a very good
idea to return a reference to a doomed object, since an unwitting caller
could get into serious trouble if they store the returned reference –
that reference will be invalid on the next line, even though there is no
obvious reason for that at the callsite.
You perhaps also remember, that the above function, with a mutable
reference, cannot be used with a temporary as its argument: like with a
constant, the compiler will complain that it cannot bind a temporary to
an argument of type int_matrix &. So is there some kind of a reference
that can bind a temporary, but not a constant? Yes, that would be an
rvalue reference, written int_matrix &&. If the above candidate fails,
the next one the compiler will look at is one with an rvalue reference as
its argument. In this case, we know the value is doomed, so we better
return a value, not a reference into the doomed matrix. Moreover,
since the input matrix is doomed anyway, we can steal the value we
are after using std::move and hence still manage to avoid a copy.
int_vector first( int_matrix &&v ) { return std::move( v[ 0 ] ); }
If both of the above fail, the value must be a constant – in this case,
we can safely return a reference into the constant. The argument is
not immediately doomed, so it is up to the caller to ensure that if they
store the reference, it does not outlive its parent object.
const int_vector &first( const int_matrix &v )
{
return v[ 0 ];
}
That concludes our quest for a polymorphic accessor. Let’s have a look
at how it works when we try to use it:
int main() /* demo */
{
int_vector v{ 3, 5, 7, 1, 4 };
assert( first( v ) == 3 );
first( v ) = 5;
assert( first( v ) == 5 );
const int_vector &const_v = v;
assert( first( const_v ) == 5 );
int_matrix m{ int_vector{ 1, 2, 3 }, v };
const int_matrix &const_m = m;
assert( first( first( m ) ) == 1 );
first( first( m ) )= 2;
assert( first( first( const_m ) ) == 2 );
assert( first( first( int_matrix{ v, v } ) ) == 5 );
What follows is the case where the rvalue-reference overload of first
(the one which handles temporaries) saves us: try to comment the
overload out and see what happens on the next 2 lines for yourself.
const int_vector &x = first( int_matrix{ v, v } );
assert( first( x ) == 5 );
}
4.d.4 [pool] This demo will be our first serious foray into dealing with
object lifetime. In particular, we will want to implement binary trees –
clearly, the lifetime of tree nodes must exactly match the lifetime of
the tree itself:
• if the nodes were released too early, the program would perform
invalid memory access when traversing the tree,
• if the nodes are not released with the tree, that would be a memory
leak – we keep the nodes around, but cannot access them.
This is an ubiquitous problem, and if you think about it, we have encountered
it a lot, but did not have to think about it yet: the characters
in an std::string or the items in an std::vector have the same property:
their lifetime must match the lifetime of the instance which owns
them.
This is one of the most important differences between C and C++: if
we do C++ right, most of the time, we do not need to manage object
lifetimes manually. This is achieved through two main mechanisms:
1. pervasive use of automatic variables, through value semantics –
local variables and arguments are automatically destroyed when
they go out of scope,
2. cascading – whenever an object is destroyed, its attributes are also
destroyed automatically, and a mechanism is provided for classes
which own additional, non-attribute objects (e.g. elements in an
std::vector) to automatically destroy them too (this is achieved
by user-defined destructors which we will explore in part 6, two
weeks from now).
In general, destroying objects at an appropriate time is the job of the
owner of the object – whether the owner is a function (this is the case
with by-value arguments and local variables) or another object (attributes,
elements of a container and so on). Additionally, this happens
transparently for the user: the compiler takes care of inserting the
right calls at the right places to ensure everything is destroyed at the
right time.
The end result is modular or composable resource management – wellbehaved
objects can be composed into well-behaved composites without
any additional glue or boilerplate.
To make things easy for now, we will take advantage of existing containers
to do resource management for us, which will save us from
writing destructors (the proverbial glue, which is boring to write and
easy to get wrong). In part 7, we will see how we can use smart pointers
for the same purpose.
We will be keeping the nodes of our binary tree in an std::vector –
this means that each node has an index which we can use to refer to
that node. In other words, in this demo (and in some of this week’s
exercises) indices will play the role of pointers. Since 0 is a valid index,
we will use -1 to indicate an invalid (‘null’) reference. Besides ‘pointers’
to the left and right child, the node will contain a single integer value.
struct node
{
int left = -1, right = -1;
int value;
};
As mentioned earlier, the nodes will be held in a vector: let’s give a
name to the particular vector type, for convenience:
using node_pool = std::vector< node >;
Working with node is, however, rather inconvenient: we cannot ‘dereference’
the left/right ‘pointers’ without going through node_pool. This
makes for verbose code which is unpleasant to both read and to write.
But we can do better: let’s add a simple wrapper class, which will remember
both a reference to the node_pool and an index of the node we
are interested in: this class can then behave like a proper reference
to node: only a value of the node_ref type is needed to access the node
and to walk the tree.
class node_ref
PB161 Programming in C++ 23/114 June 28, 2022
{
node_pool &_pool;
int _idx;
To make the subsequent code easier to write (and read), we will define
a few helper methods: first, a get method which returns an actual
reference to the node instance that this node_ref represents.
node &get() { return _pool[ _idx ]; }
And a method to construct a new node_ref using the same pool as this
one, but with a new index.
node_ref make( int idx ) { return { _pool, idx }; }
Normally, we do not want to expose the _pool or node to users directly,
hence we keep them private. But it’s convenient for tree itself to be
able to access them. So we make tree a friend.
friend class tree;
public:
node_ref( node_pool &p, int i ) : _pool( p ), _idx( i ) {}
For simplicity, we allow invalid references to be constructed: those
will have an index -1, and will naturally arise when we encounter a
node with a missing child – that missing node is represented as index
-1. The valid method allows the user to check whether the reference
is valid. The remaining methods (left, right and value) must not be
called on an invalid node_ref. This is the moral equivalent of a null
pointer.
bool valid() const { return _idx >= 0; }
What follows is a simple interface for traversing and inspecting the
tree. Notice that left and right again return node_ref instances. This
makes tree traversal simple and convenient.
node_ref left() { return make( get().left ); }
node_ref right() { return make( get().right ); }
int &value() { return get().value; }
};
Finally the class to represent the tree as a whole. It will own the
nodes (by keeping a node_pool of them as an attribute, will remember
a root node (which may be invalid, if the tree is empty) and provide an
interface for adding nodes to the tree. Notice that removal of nodes is
conspicuously missing: that’s because the pool model is not well suited
for removals (smart pointers will be better in that regard).
class tree
{
node_pool _pool;
int _root_idx = -1;
A helper method to append a new node to the pool and return its index.
int make( int value )
{
_pool.emplace_back();
_pool.back().value = value;
return _pool.size() - 1;
}
public:
node_ref root() { return { _pool, _root_idx }; }
bool empty() const { return _root_idx == -1; }
We will use a vector to specify a location in the tree for adding a node,
with values -1 (left) and 1 (right). An empty vector represents at the
root node.
using path_t = std::vector< int >;
Find the location for adding a node recursively and create the node
when the location is found. Assumes that the path is correct.
void add( node_ref parent, path_t path, int value,
unsigned path_idx = 0 )
{
assert( path_idx < path.size() );
int dir = path[ path_idx ];
if ( path_idx < path.size() - 1 )
{
auto next = dir < 0 ? parent.left() : parent.right();
return add( next, path, value, path_idx + 1 );
}
if ( dir < 0 )
parent.get().left = make( value );
else
parent.get().right = make( value );
}
Main entry point for adding nodes.
void add( path_t path, int value )
{
if ( root().valid() )
add( root(), path, value );
else
{
assert( path.empty() );
_root_idx = make( value );
}
}
};
int main() /* demo */
{
tree t;
t.add( {}, 1 );
assert( t.root().value() == 1 );
assert( t.root().valid() );
assert( !t.root().left().valid() );
t.add( { -1 }, 7 );
assert( t.root().value() == 1 );
assert( t.root().left().valid() );
assert( t.root().left().value() == 7 );
t.add( { -1, 1 }, 3 );
assert( t.root().left().right().value() == 3 );
}
Part 4.e: Elementary Exercises
4.e.1 [diameter] Standard point in a plane, with x and y coordinates,
stored as double-precision floating point numbers, with the obvious
constructor.
struct point;
Define a structure which describes a circle with a given center and a
given radius (a point and a non-negative number). Include a straightforward
constructor.
struct circle_radius;
And a structure, which describes a circle using two points: the center
and a point on the circle. Again, add a constructor.
struct circle_point;
Finally, define function diameter which given either of the above rep-
PB161 Programming in C++ 24/114 June 28, 2022
resentations of a circle, returns its diameter (i.e. twice the radius).
// double diameter( ??? );
4.e.2 [circle] Standard 2D point.
struct point;
Implement a structure circle with 2 constructors, one of which accepts
a point and a number (center and radius) and another which accepts 2
points (center and a point on the circle itself). Store the circle using its
center and radius, in attributes center and radius respectively.
struct circle;
4.e.3 [index] In this exercise, you will provide index-based access to
pairs and vectors of integers, using function overloading. The element
function should take an std::vector or an std::pair as its first argument
and an index as its second argument. A companion size function
should return the number of valid indices for either of the two types
of objects.
// ??? element( ???, int idx );
// ??? size( ??? );
Part 4.p: Preparatory Exercises
4.p.1 [format] In this exercise, we will implement a very simple ‘string
builder‘: a class that will help us create strings from smaller pieces.
It will have a single overloaded method called add, in 3 variants: it
will accept either a string, an integer or a floating-point number (use
std::to_string for conversions).
To make it easier to use, add should return a reference to the instance it
was called on. See below for examples. The method get should return
the constructed string.
class string_builder;
4.p.2 [least] The class element represents a value which, for whatever
reason, cannot be duplicated. Our goal will be to write a function
which takes a vector of these, finds the smallest and returns it. Do not
change the definition of element in any way.
class element
{
int value;
public:
element( int v ) : value( v ) {}
element( element &&v ) : value( v.value ) {}
element &operator=( element &&v ) = default;
bool less_than( const element &o ) const { return value <
o.value; }
bool equal( const element &o ) const { return value == o.value;
}
};
using data = std::vector< element >;
Write function least (or a couple of function overloads) so that calling
least( d ) where d is of type data returns the least element in the input
vector.
// ??? least( ??? )
4.p.3 [area] Implement 2 classes which represent 2D shapes: (regular)
polygon and circle. Each of the shapes has 2 constructors:
• circle takes either 2 points (center and a point on the circle) or a
point and a number (radius),
• polygon takes an integer (the number of sides ≥ 3) and either two
points (center and a vertex) or a single point and a number (the
major radius).
Add a toplevel function area which can compute the area of either.
struct point;
struct polygon;
struct circle;
4.p.4 [zipper] In this exercise, we will implement a simple data structure
called a zipper – a sequence of items with a single focused item.
Since we can’t write class templates yet, we will just make a zipper of
integers. Our zipper will have these operations:
• (constructor) constructs a singleton zipper from an integer
• shift_left and shift_right move the point of focus, in O(1), to the
nearest left (right) element; they return true if this was possible,
otherwise they return false and do nothing
• insert_left and insert_right add a new element just left (just right)
of the current focus, again in O(1)
• focus access the current item (read and write)
• bonus: add erase_left and erase_right to remove elements around
the focus (return true if this was possible), in O(1)
class zipper;
4.p.5 [rpn] Write a simple stack-based evaluator for numeric expressions
in an RPN form. The operations:
• push takes a number and pushes it onto the working stack,
• apply accepts an instance of one of the three operator classes defined
below; like with the string builder earlier, both those methods
should return a reference to the evaluator,
• again like with the zipper, a top method should give access to the
current top of the stack, including the possibility of changing the
value,
• pop which also returns the popped value, and
• empty which returns a bool.
All three operators are binary (take 2 arguments).
struct add {}; /* addition */
struct mul {}; /* multiplication */
struct dist {}; /* absolute value of difference */
class eval;
4.p.6 [eval] We will do an infix version of the evaluator from the
previous exercise. Additionally, we will want to store common subexpressions
only once. For this reason, we will store the nodes in a
pool and only take out references to them.
struct node
{
The type of the node. Only mul and add nodes have children.
enum op_t { mul, add, constant } op;
The attributes left and right are indices, with -1 indicating an invalid
(null) reference. The is_root boolean indicates whether this node is a
root – that is, it does not appear as a child of any other node.
int left = -1, right = -1;
bool is_root = true;
The value stored in a constant-type node.
int value = 0;
};
using node_pool = std::vector< node >;
An ‘ephemeral’ reference to a node – one that can be used to traverse
PB161 Programming in C++ 25/114 June 28, 2022
an expression tree, but which is only valid as long as the eval instance
which created it is alive. Add const methods left(), right() which return
another node_ref instance, a const method compute() which evaluates
the subtree, and a non-const method update( int ) which only
works on nodes of type constant.
class node_ref;
The eval class represents an entire expression which can be evaluated,
traversed (starting from root nodes – those which have no parent) and,
most importantly, extended by creating new nodes.
class eval
{
node_pool _pool;
public:
std::vector< node_ref > roots();
node_ref add( node_ref, node_ref );
node_ref mul( node_ref, node_ref );
node_ref number( int );
};
Part 4.r: Regular Exercises
4.r.1 [complex] Structure angle simply wraps a single double-precision
number, so that we can use constructor overloads to allow use of both
polar and cartesian forms to create instances of a single type (complex).
struct angle;
struct complex;
Now implement the following two functions, so that they work both
for real and complex numbers.
// double magnitude( … )
// … reciprocal( … )
The following two functions only make sense for complex numbers,
where arg is the argument, normalized into the range (−π, π⟩:
double real( complex );
double imag( complex );
double arg( complex );
4.r.2 [bsearch] Implement binary search on a vector. Both constant
and mutable vectors should be accepted (by reference) and an appropriate
iterator type (iterator or const_iterator) should be returned. Try
to avoid code duplication. Return end if the element is not found.
4.r.3 [search] Implement a binary search tree, i.e. a binary tree which
maintains the search property. That is, a value of each node is:
• ≥ than all values in its left subtree,
• ≤ than all values in its right subtree.
Store the nodes in a pool (a vector or a list, your choice). The interface
is as follows:
• node_ref root() const returns the root node,
• bool empty() const checks whether the tree is empty,
• void insert( int v ) inserts a new value into the tree (without re-
balancing).
The node_ref class then ought to provide:
• node_ref left() const and node_ref right() const,
• bool valid() const,
• value() const which returns the value stored in the node.
Calling root on an empty tree is undefined.
struct node; /* ref: 6 lines */
using node_pool = std::vector< node >;
class node_ref; /* ref: 12 lines */
class tree; /* ref: 28 lines */
std::tuple< bool, int, int > verify( node_ref n, int bound );
bool has( node_ref n, int v );
4.r.4 [bitptr] Implement 2 classes, bitptr and const_bitptr, which provide
access to a single (mutable or constant) bit. Instances of these
classes should behave as pointers in principle, though we don’t yet
have tools to make them behave this way syntactically (that comes
next week). In the meantime, let’s use the following interface:
• bool get() – read the pointed-to bit,
• void set( bool ) – write the same,
• void advance() – move to the next bit,
• void advance( int ) – move by a given number of bits,
• bool valid() – is the pointer valid?
A default-constructed bitptr is not valid. Moving an invalid bitptr
results in another invalid bitptr. Otherwise, a bitptr is constructed
from a std::byte pointer and an int with value between 0 and 7 (with 0
being the least-significant bit). A bitptr constructed this way is always
considered valid, regardless of the value of the std::byte pointer passed
to it.
class bitptr;
class const_bitptr;
4.r.5 [sort] Implement sort which works both on vectors (std::vector)
and linked lists (std::list) of integers. The former should use in-place
quicksort, while the latter should use merge sort (it’s okay to use the
splice and merge methods on lists, but not sort). Feel free to refer back
to 01/r5 for the quicksort.
Part T.1: Introductory Tasks
The programming tasks for this block are as follows:
1. cellular.* – a simple cellular automaton simulator,
2. magic.* – a backtracking magic square solver,
3. reversi.* – a 3D version of the game reversi,
4. chess.* – a simple simulator of standard chess.
In this set, the tasks only require basic programming skills and C++
constructs that you have encountered in the first two chapters. In
other words, no advanced language constructs or library features are
necessary.
Part T.1.1: [cellular]
The goal of this task is to implement a simulator for one-dimensional
cellular automata. You will implement this simulator as a class, the
interface of which is described below You are free to add additional
methods and data members to the class, and additional classes and
functions to the file, as you see fit. You must, however, keep the entire
interface in this single file. The implementation can be in either
cellular.hpp or in cellular.cpp. Only these two files will be submitted.
The class automaton_state represents the state of a 1D, infinite binary
cellular automaton. The set and get methods can be passed an arbi-
PB161 Programming in C++ 26/114 June 28, 2022
trary index.
class automaton_state
{
Attributes are up to you.
public:
automaton_state(); /* create a blank state (all cells are 0) */
void set( int index, bool value ); /* change the given cell */
bool get( int index ) const;
};
The automaton class represents the automaton itself. The automaton is
arranged as a cross, with a horizontal and a vertical automaton, which
are almost entirely independent (each has its own state and its own
rule), with one twist: the center cell (index 0 in both automata) is shared.
The new state of the shared center cell (after a computation step is
performed in both automata independently) is obtained by combining
the two values (that either automaton would assign to that cell) using
a specified boolean binary operator. The new center is obtained as
horizontal_center OP vertical_center. The state can look, for example,
like this:
…01
…
1
0
1
0
1
…
00…
The automaton keeps its state internally and allows the user to perform
simulation on this internal state. Initially, the state of the automaton is
0 (false) everywhere. The rules for both the vertical and the horizontal
component are given to the constructor by their Wolfram code.
The center-combining operator is given by the same type of code, but
instead of 3 cells, only 2 need to be combined: there are only 16 such
operators (compared to 256 rules for each of the automata). The input
vectors to the binary operator are numbered by their binary code as:
left right index
0 0 0
0 1 1
1 0 2
1 1 3
The operator code is then a 4-digit binary number, e.g 0110 gives the
code for xor (0 0 → 0, 0 1 → 1, 1 0 → 1, 1 1 → 0) while 1000 gives code
for and (everything is zero except if both inputs are 1). And so on and
so forth. The same process but with 3 input cells is used to construct
the Wolfram code for the automata.
class automaton
{
Attributes are up to you.
public:
enum direction { vertical, horizontal };
Constructs an automaton based on a rule given by its Wolfram code
for the horizontal component, another for the vertical component, and
a 4-bit code for the center operator. Assume that neither of the rules
contains the transition 000 → 1.
automaton( int h_rule, int v_rule, int center );
The read method returns the current value of the (shared) center cell.
The set method sets the specified cell to the value given.
bool read() const;
void set( direction dir, int index, bool value );
Finally, the following methods run the simulation – either perform a
single step (update each cell exactly once) or a given number of steps
(assume a non-negative number of steps).
void step();
void run( int steps );
};
The compute_cell function takes two rule numbers, two initial states,
a center operator and a number of steps. It then computes the value
of the central cell after n steps of the automaton such described. Like
above, the number of steps is a non-negative number. Assume that
the center cell in both input states has the same value.
bool compute_cell( int vertical_rule, int horizontal_rule,
int center_op,
const automaton_state &vertical_state,
const automaton_state &horizontal_state,
int steps );
Part T.1.2: [chess]
The goal of this task is to implement the standard rules of chess.
struct position
{
int file; /* column 'letter', a = 1, b = 2, ... */
int rank; /* row number, starting at 1 */
};
enum class piece_type
{
pawn, rook, knight, bishop, queen, king
};
enum class player { white, black };
The following are the possible outcomes of play. The outcomes are
shown in the order of precedence, i.e. the first applicable is returned.
capture the move was legal and resulted in a capture
ok the move was legal and was performed
no_piece there is no piece on the from square
bad_piece the piece on from is not ours
bad_move this move is not available for this piece
blocked another piece is in the way
lapsed en passant capture is no longer allowed
has_moved one of the castling pieces has already moved
in_check the player is currently in check and the
move does not get them out of it
would_check the move would place the player in check
bad_promote promotion to a pawn or king was attempted
Attempting an en passant when the pieces are in the wrong place is a
bad_move. In addition to has_moved, (otherwise legal) castling may give:
• blocked – some pieces are in the way,
• in_check – the king is currently in check,
• would_check – would pass through or end up in check.
enum class result
PB161 Programming in C++ 27/114 June 28, 2022
{
capture, ok, no_piece, bad_piece, bad_move, blocked, lapsed,
in_check, would_check, has_moved, bad_promote
};
struct occupant
{
bool is_empty;
player owner;
piece_type piece;
};
class chess
{
public:
Construct a game of chess in its default starting position. The first call
to play after construction moves a piece of the white player.
chess();
Move a piece currently at from to square to:
• in case the move places a pawn at its 8th rank (rank 8 for white, rank
1 for black), it is promoted to the piece given in promote (otherwise,
the last argument is ignored),
• castling is described as a king move of more than one square,
• if the result is an error (not capture nor ok), calling play again will
attempt another move by the same player.
result play( position from, position to,
piece_type promote = piece_type::pawn );
Which piece is at the given position?
occupant at( position ) const;
};
Part T.1.3: [magic]
A magic square is an n × n grid of natural numbers 1–n2
, such that all
rows and columns and both diagonals add up to a fixed ‘magic constant’
and each number appears exactly once. Solving the square means
filling in all empty cells in a manner that gives the full square the magic
property. The goal of this task is to implement a simple backtracking
solver for completing partially filled magic squares.
class magic
{
public:
Construct an empty n × n square.
magic( int n );
Get the value at the given position. A return value of 0 indicates an
empty square.
int get( int x, int y ) const;
Set a cell at the given position to a given value. The behaviour is
undefined if v is already present in the square. If v is negative, the
cell is empty, but must not take std::abs( v ) as its value in the solved
square.
void set( int x, int y, int v );
Solve the square: fill in all empty cells so that the square has the magic
property and return true. If the square cannot be solved, do not change
its content and return false.
bool solve();
};
Part T.1.4: [reversi]
The subject of this task is the game of reversi (also known as othello),
played by two players on a 3D board (a box) of a given shape (given as
3 even, non-negative numbers). Size 0 in a given direction means the
board is infinite in that direction.
The cells are cubes (a cube has 8 vertices, 12 edges and 6 faces). The
coordinates start at the center (which is a vertex) and extend in two
directions (positive and negative) along the 3 axes. The 8 cells which
share the center vertex have coordinates [1, 1, 1], [1, 1, -1], [1, -1, 1], [1, -1,
-1], …
The rules are a straightforward extension of the standard 2D rules
into three dimensions:
• each player starts with 4 stones placed around the center such that
no two (of the same colour) share a face, with white taking the [1, 1,
1] cell,
• players take turns in placing a new stone, which must be placed
adjacent (share an edge, vertex or a face) to an opposing player’s
stone, and enemy stones must form a straight, uninterrupted line
to one of current players’ own stones (along straight lines – sharing
a face, along diagonals which share an edge, or along diagonals
which share a vertex),
• the colour of all opposing stones on all such lines connecting the
new stone to existing stones of the current player is flipped.
The white player starts. The game ends when no new stones can be
placed and the player with more stones wins. It must be possible to
make a copy of an in-progress game.
class reversi
{
public:
reversi( int x_size, int y_size, int z_size );
Place a stone at the given coordinates. If the placement was legal,
returns true and the next call places a stone of the opposing player;
otherwise, no change is made, the function returns false and the same
player must try a different move.
As a special case, if the current player has no legal move left, but the
game is not finished, play must be called with x = y = z = 0 to
continue. Doing this is illegal in any other circumstances.
It is undefined behaviour to call play when the game is already over.
bool play( int x, int y, int z );
Return true if the game is finished (no further moves are possible).
bool finished() const;
Only defined if the game is already over (i.e. finished would return
true). Returns the difference in the number of stones of each player:
positive for white’s victory, negative for black’s victory, 0 for a draw.
int result() const;
};
PB161 Programming in C++ 28/114 June 28, 2022
Part 5: Operators and IO
The main topics for week 5 are operator overloading (which will build
on what we learned about function and method overloading in week
4). The second topic for this week will be IO: we will look at formatted
input and output and at reading and writing files.
Demonstrations:
1. arithmetic – introduction to operator overloading,
2. relational – implementing equality and ordering,
3. access – dereference, indexing and other access ops,
4. convert – conversion and assignment,
5. files – opening files, reading and writing strings
6. streams – from values to strings and back
7. format – overloading formatting operators
Elementary exercises:
1. cartesian – complex numbers in algebraic form,
2. force – composing and scaling forces,
3. forcefmt – vectors redux, this time with IO
Preparatory exercises:
1. polar – complex numbers in polar form,
2. rational – rational numbers with ordering,
3. tmpfile – an auto-erasing temporary file
4. nibble – a pointer-like class for sub-byte access,
5. grep – print matching lines
6. fixnum – more numbers, this time with a parser.
Regular exercises:
1. poly – polynomials with addition and multiplication
2. csv – parse comma-separated numeric data
3. set – a set of integers with set operators,
4. email – a simplified RFC 822 parser
5. json – format a string → string map as JSON
6. cpp † – a very simple C preprocessor
Part 5.d: Demonstrations
5.d.1 [arithmetic] Operator overloading allows instances of classes to
behave more like built-in types: it makes it possible for values of custom
types to appear in expressions, as operands. Before we look at examples
of how this looks, we need to define a class with some overloaded
operators. For binary operators, it is customary to define them using a
‘friends trick’, which allows us to define a top-level function inside a
class.
As a very simple example, we will implement a class which represents
integral values modulo 7 (this happens to be a finite field, with addition
and multiplication).
class gf7
{
int value;
public:
The constructor is trivial, it simply constructs a gf7 instance from an
integer. We mark it explicit to avoid surprising automatic conversions
of integers into gf7 instances.
explicit gf7( int v ) : value( v % 7 ) {}
This is the ‘friend trick’ syntax for writing operators, and for binary
operators, it is often the preferred one (because of its symmetry). The
function is not really a part of the class in this case – the trick is that
we can write it here anyway.
friend gf7 operator+( gf7 a, gf7 b )
{
return gf7( a.value + b.value ); // [a]₇ + [b]₇ = [a + b]₇
}
For multiplication, we will use the more ‘orthodox‘ syntax, where the
operator is a const method: the left operand is passed into the operator
as this, the right operand is the argument. In general, operatorsas-methods
have one explicit argument less (unary operators take 0
arguments, binary take 1 argument).
gf7 operator*( gf7 b ) const
{
return gf7( value * b.value ); // [a]₇ * [b]₇ = [a * b]₇
}
Values of type gf7 cannot be directly compared (we did not define
the required operators) – instead, we provide this method to convert
instances of gf7 back into int’s.
int to_int() const { return value; }
};
Operators can be also overloaded using ‘normal’ top-level functions,
like this unary minus (which finds the additive inverse of the given
element). Notice that we cannot access private fields (attributes) of the
class here:
gf7 operator-( gf7 x ) { return gf7( 7 - x.to_int() ); }
Now that we have defined the class and the operators, we can look at
how is the result used.
int main() /* demo */
{
gf7 a( 3 ), b( 4 ), c( 0 ), d( 5 );
Values a, b and so forth can be now directly used in arithmetic expressions,
just as we wanted.
gf7 x = a + b;
gf7 y = a * b;
Let us check that the operations work as expected:
assert( x.to_int() == c.to_int() ); /* [3]₇ + [4]₇ = [0]₇ */
assert( y.to_int() == d.to_int() ); /* [3]₇ * [4]₇ = [5]₇ */
assert( (-a + a).to_int() == c.to_int() ); /* unary minus */
}
That was arithmetic operator overloading. Let’s now look at relational
(ordering) operators, in relational.cpp.
5.d.2 [relational] In this example, we will show relational operators,
which are very similar to the arithmetic operators from previous example,
except for their return types, which are bool values.
The example which we will use in this case are sets of small natural
numbers (1-64) with inclusion as the order. We will implement the full
set of comparison operators, which is still required in C++17 but will
no longer be needed in C++20 (with the spaceship operator).
NB. Standard ordered containers like std::set and std::map require the
operator less-than to define a linear order. The comparison operators
in this example do not define a linear order.
class set
{
Each bit of the below number indicates the presence of the corresponding
integer (the index of that bit) in the set.
uint64_t bits;
public:
PB161 Programming in C++ 29/114 June 28, 2022
Like before, we add an explicit constructor that takes an initial value.
We use a default argument to say that the constructor can be used as
a default constructor (without arguments), in which case it will create
an empty set.
explicit set( uint64_t to_set = 0 ) : bits( to_set ) {}
We also define a few methods to add and remove numbers from the
set, to test for presence of a number and an emptiness check.
void add( int i ) { bits |= 1ul << i; }
void del( int i ) { bits &= ~( 1ul << i ); }
bool has( int i ) const { return bits & ( 1ul << i ); }
bool empty() const { return !bits; }
We will use the method syntax here, because it is slightly shorter. We
start with (in)equality, which is very simple (the sets are equal when
they have the same members):
bool operator==( set b ) const { return bits == b.bits; }
bool operator!=( set b ) const { return bits != b.bits; }
It will be quite useful to have set difference to implement the comparisons
below, so let us also define that:
set operator-( set b ) const { return set( bits & ~b.bits ); }
Since the non-strict comparison (ordering) operators are easier to implement,
we will do that first. Set b is a superset of set a if all elements
of a are also present in b, which is the same as the difference a - b
being empty.
bool operator<=( set b ) const { return ( *this - b ).empty(); }
bool operator>=( set b ) const { return ( b - *this ).empty(); }
};
And finally the strict comparison operators, which are more conveniently
written using top-level function syntax:
bool operator<( set a, set b ) { return a <= b && a != b; }
bool operator>( set a, set b ) { return a >= b && a != b; }
int main() /* demo */
{
set a; a.add( 1 ); a.add( 7 ); a.add( 13 );
set b; b.add( 1 ); b.add( 6 ); b.add( 13 );
In each pair of assertions below, the two expressions are not quite
equivalent. Do you understand why?
assert( a != b ); assert( !( a == b ) );
assert( a == a ); assert( !( a != a ) );
The two sets are incomparable, i.e. neither is less than the other, but
as shown above they are not equal either.
assert( !( a < b ) ); assert( !( b < a ) );
a.add( 6 ); // let's make ‹a› a superset of ‹b›
And check that the ordering operators work on ordered sets.
assert( a > b ); assert( a >= b ); assert( a != b );
assert( b < a ); assert( b <= a ); assert( b != a );
b.add( 7 ); /* let's make the sets equal */
assert( a == b ); assert( a <= b ); assert( a >= b );
}
That’s all regarding relational operators, you will have a chance to
implement your own in one of the exercises later. In the meantime,
let us move on to ‘access’ operators: dereference, indirect access and
indexing, in access.cpp.
5.d.3 [access] This set of operators will be slightly more difficult.
Surely, you remember the unary * operator from C, where it is used
to dereference pointers. We haven’t seen much of that in C++, except
perhaps with iterators. We will now see how to implement a class
which can be dereferenced like a pointer. We will also add indexing to
the mix (like with plain C arrays, or std::vector or even std::map).
Let us revisit the zipper class from last week. We will add indexing
(relative to the focus), use a dereference operator to access the focus
and we will not store integers, but points in a plane. Cue our favourite
class, a point:
struct point
{
double x, y;
point( double x, double y ) : x( x ), y( y ) {}
We know equality comparison from previous examples. We will need
it later on for writing test cases for zipper.
bool operator==( point o ) const { return x == o.x && y == o.y;
}
};
Now for the zipper. We will need to use std::vector to be able to index
elements, but we will still use left and right like stacks.
class zipper
{
using stack = std::vector< point >;
stack left, right;
point focus;
public:
zipper( double x, double y ) : focus( x, y ) {}
Inserting points into the zipper.
zipper &emplace_left( double x, double y )
{
left.emplace_back( x, y );
return *this;
}
zipper &emplace_right( double x, double y )
{
right.emplace_back( x, y );
return *this;
}
A helper method, so we don’t repeat ourselves in the increment/decrement
operators below. The trick is to pass the left/right stacks by
reference, since moving left and right is symmetric with regards to
those (i.e. the code to move left is the same as to move right, with all
occurrences of left and right swapped).
void shift( stack &a, stack &b )
{
b.push_back( focus );
focus = a.back();
a.pop_back();
}
First the pre-increment operators, i.e. ++x and --x. Here, we use those
operators in the manner of C pointer arithmetic (you may want to
review that topic).
zipper &operator++() { shift( right, left ); return *this; }
zipper &operator--() { shift( left, right ); return *this; }
Now the post-increment: x++ and x--. In this particular data structure,
they are expensive and should not be used. They are here just to
demonstrate the syntax and a common implementation technique.
The difference is that post-increment needs to make a copy, since the
PB161 Programming in C++ 30/114 June 28, 2022
value of the expression is the object before the increment/decrement
was applied to it.
zipper operator++( int ) { auto r = *this; ++*this; return r; }
zipper operator--( int ) { auto r = *this; --*this; return r; }
The dereference (unary *) and indirect member access operators (mutable,
i.e. non-const overloads first, then the const overloads). Those
operators allow us to treat zipper as if it was a pointer to a point instance
(the one that is in focus). See main below to see how this works
when used.
point &operator*() { return focus; }
point *operator->() { return &focus; }
const point &operator*() const { return focus; }
const point *operator->() const { return &focus; }
And finally an indexing operator. We will not bother with the const
version at this time: it would be certainly possible, but ugly and/or
repetitive.
point &operator[]( int i )
{
if ( i == 0 ) return focus;
if ( i < 0 ) return left[ left.size() + i ];
if ( i > 0 ) return right[ right.size() - i ];
assert( false );
}
};
int main() /* demo */
{
zipper z( 0, 0 ); // [0,0]
Notice the correspondence between *x and x[ 0 ] that we carried over
from C pointers.
assert( z[ 0 ] == point( 0, 0 ) );
assert( *z == point( 0, 0 ) );
We will add a few items to the zipper, so that we can demonstrate the
other operators.
z.emplace_left( 1, 1 ); // (1,1) [0,0]
z.emplace_right( 2, 1 ); // (1,1) [0,0] (2,1)
Check that the indexing operators behave as expected: negative indices
give us items on the left and positive indices give us items on the right.
assert( z[ -1 ] == point( 1, 1 ) );
assert( z[ 1 ] == point( 2, 1 ) );
Let us check that indexing also works further out.
z.emplace_left( 2, 2 ); // (1,1) (2,2) [0,0] (2,1)
assert( z[ -2 ] == point( 1, 1 ) );
assert( z[ -1 ] == point( 2, 2 ) );
The pre-decrement operator moves the focus of the zipper tho the left.
Let’s check that (and demonstrate the correspondence between z[ 0 ]
and *z again, for a good measure).
-- z; // (1,1) [2,2] (0,0) (2,1)
assert( z[ -1 ] == point( 1, 1 ) );
assert( z[ 0 ] == point( 2, 2 ) );
assert( *z == point( 2, 2 ) );
Finally the indirect access operators let us look at x and y of the focused
point in a nice, succinct way. The syntax is the same that you used to
access struct members via a pointer to the struct in C.
assert( z->x == 2 );
assert( z->y == 2 );
Move the zipper twice to the right and do a final check.
++ z; ++ z; // (1,1) (2,2) (0,0) [2,1]
assert( z->x == 2 );
assert( z->y == 1 );
}
Next: quick introduction to exceptions, in exceptions.cpp.
5.d.4 [convert] In this example, we will implement a class which behaves
like a nullable reference to an integer. Taking a hint from Java,
we will throw an exception when the user attempts to use a null refer-
ence.
We first define the type which we will use to indicate an attempt to
use an invalid (null) reference.
class null_pointer_exception {};
Now for the reference-like class itself. We need two basic ingredients
to provide simple reference-like behaviours: we need to be able to
(implicitly) convert a value of type maybe_ref to a value of type int.
The other part is the ability to assign new values of type int to the
referred-to variable, via instances of the class maybe_ref.
class maybe_ref
{
We hold a pointer internally, since real references in C++ cannot be
null.
int *_ptr = nullptr;
We will also define a helper (internal, private) method which checks
whether the reference is valid. If the reference is null, it throws the
above exception.
void _check() const
{
if ( !_ptr )
throw null_pointer_exception();
}
public:
Constructors: the default-constructed maybe_ref instances are nulls,
they have nowhere to point. Like real references in C++, we will allow
maybe_ref to be initialized to point to an existing value. We take the
argument by reference and convert that reference into a pointer by
using the unary & operator, in order to store it in _ptr.
maybe_ref() = default;
maybe_ref( int &i ) : _ptr( &i ) {}
As mentioned earlier, we need to be able to (implicitly) convert
maybe_ref instances into integers. The syntax to do that is operator
type, without mentioning the return type (in this case, the return type
is given by the name of the operator, i.e. int here). It is also possible
to have reference conversion operators, by writing e.g. operator const
int &(). However, we don’t need one of those here because int is small,
and we can’t have both since that would cause a lot of ambiguity.
operator int() const
{
_check();
return *_ptr;
}
The final part is assignment: as you have learned in the lecture, operator=
should return a reference to the assigned-to instance. It usually
takes a const reference as an argument, but again we do not need to do
that here. Below in the demo, we will point out where the assignment
PB161 Programming in C++ 31/114 June 28, 2022
operator comes into play.
maybe_ref &operator=( int v )
{
_check();
*_ptr = v;
return *this;
}
};
int main() /* demo */
{
int i = 7;
When initializing built-in references, we use int &i_ref = i. We can
do the same with maybe_ref, but we need to keep in mind that this
syntax calls the maybe_ref( int ) constructor, not the assignment op-
erator.
maybe_ref i_ref = i;
Let us check that the reference behaves as expected.
assert( i_ref == 7 ); /* uses conversion to ‹int› */
i_ref = 3; /* uses the assignment operator */
assert( i_ref == 3 ); /* conversion to ‹int› again */
Check that the original variable has changed too.
assert( i == 3 );
Let’s also check that null references behave as expected.
bool caught = false;
maybe_ref null;
Comparison will try to convert the reference to int, but that will fail
in _check with an exception.
try { assert( null == 7 ); }
catch ( const null_pointer_exception & ) { caught = true; }
Make sure that the exception was thrown and caught.
assert( caught );
caught = false;
Same but with assignment into the null referenc.
try { null = 2; }
catch ( const null_pointer_exception & ) { caught = true; }
assert( caught );
}
5.d.5 [files] This example will be brief: we will show how to open a
file for reading and fetch a line of text. We will then write that line of
text into a new file and read it back again to check that things worked.
We will split up the example into functions for 2 reasons: first, to
make it easier to follow, and second, to take advantage of RAII: the file
streams will close the underlying resource when they are destroyed.
In this case, that will be at the end of each function.
std::string read( const char *file )
{
The default method of doing IO in C++ is through streams. Reading
files is done through a stream of type std::ifstream, which is short for
input file stream. The constructor of ifstream takes the name of the
file to open. We will use a file given to us by the caller.
std::ifstream f( file );
The simplest method to read text from a file is using std::getline,
which will fetch a single line at a time, into an std::string. We need
to prepare the string in advance, since it is passed into std::getline as
an output argument.
std::string line;
The std::getline function returns a reference to the stream that was
passed to it. Additionally, the stream can be converted to bool to find
out whether everything is okay with it. If the reading fails for any
reason, it will evaluate to false. The newline character is discarded.
if ( !std::getline( f, line ) )
In real code, we would of course want to handle errors, because opening
files is something that can fail for a number of reasons. Here, we
simply assume that everything worked.
assert( false );
return line;
}
Next comes a function which demonstrates writing into files.
void write( const char *file, std::string line )
{
To write data into a file, we can use std::ofstream, which is short for
output file stream. The output file is created if it does not exist.
std::ofstream f( file );
Writing into a file is typically done using operators for formatted output.
We will look at those in more detail in the next section. For now,
all we need to know that writing an object into a stream is done like
this:
f << line;
We will also want to add the newline character that getline above
chomped. We have two options: either use the "\n" string literal, or
std::endl – a so-called stream manipulator which sends a newline
character and asks the stream to send the bytes to the operating system.
Let’s try the more idiomatic approach, with the manipulator:
f << std::endl;
At this point, the file is automatically closed and any outstanding data
is sent to the operating system.
}
int main() /* demo */
{
We first use read to get the first line of this file.
std::string line = read( "d5_files.cpp" );
And we check that the line we got is what we expect. Remember the
stripped newline.
assert( line == "/* This example will be brief:"
" we will show how to open a file for" );
Now we write the line into another file. After you run this example,
you can inspect files.out with an editor. It should contain a copy of
the first line of this file.
write( "d5_files.out", line );
Finally, we use read again to read "file.out" back, and check that the
same thing came back.
std::string check = read( "d5_files.out" );
PB161 Programming in C++ 32/114 June 28, 2022
assert( check == line );
}
5.d.6 [streams] File streams are not the only kind of IO streams that
are available in the standard library. There are 3 ‘special’ streams,
called std::cout, std::cerr and std::cin. Those are not types, but
rather global variables, and represent the standard output, the standard
error output and the standard input of the program. However,
the first two are instances of std::ostream and the third is an instance
of std::istream.
We don’t know about class inheritance yet, but it is probably not a
huge stretch to understand that instances of std::ofstream (output file
stream) are also at the same time instances of std::ostream (general output
stream). The same story holds for std::ifstream (input file stream)
and std::istream (general input stream).
There is another pair of classes: std::ostringstream and
std::istringstream. Those streams are not attached to OS resources,
but to instances of std::string: in other words, when you write to an
ostringstream, the resulting bytes are not sent to the operating system,
but are instead appended to the given string. Likewise, when you
read from an istringstream, the data is not pulled from the operating
system, but instead come from an std::string. Hopefully, you can
see the correspondence between files (the content of which are byte
sequences stored on disk) and strings (the content of which are byte
sequences stored in RAM).
In any case, string streams are ideal for playing around, because we
can use the same tools as we always do: create some simple instances,
apply operations and use assert to check that the results are what we
expect. String-based streams are defined in the header sstream.
Everything that we will do with string streams applies to other types
of streams too (i.e. the 3 special streams mentioned earlier, and all file
streams).
Like in the previous example, we will split up the demonstration into
a few sections, mainly to avoid confusion over variable names. We
will first demonstrate reading from streams. We have already seen
std::getline, so let’s start with that. It is probably noteworthy that it
works on any input stream, not just std::ifstream.
void getline_1()
{
std::istringstream istr( "a string\nwith 2 lines\n" );
std::string s;
assert( std::getline( istr, s ) );
assert( s == "a string" );
assert( std::getline( istr, s ) );
assert( s == "with 2 lines" );
assert( !std::getline( istr, s ) );
assert( s.empty() );
}
We can also override the delimiter character for std::getline, to extract
delimited fields from input streams.
void getline_2()
{
std::istringstream istr( "colon:separated fields" );
std::string s;
assert( std::getline( istr, s, ':' ) );
assert( s == "colon" );
assert( std::getline( istr, s, ':' ) );
assert( s == "separated fields" );
assert( !std::getline( istr, s, ':' ) );
}
So far so good. Our other option is so-called formatted input. The
standard library doesn’t offer much in terms of ready-made overloads
for such inputs: there is one for strings, which extracts individual
words (like the scanf specifier %s, if you remember that from C, but
the C++ version is actually safe and it is okay to use it). Then there is
an instance for char, which extracts a single character (regardless of
whether it is a whitespace character or not) and a bunch of overloads
for various numeric types.
void formatted_input()
{
std::istringstream istr( "integer 123 float 3.1415 s t" );
std::string s, t;
int i; float f;
istr >> s; assert( s == "integer" );
istr >> i; assert( i == 123 );
istr >> s; assert( s == "float" );
Notice that float numbers are not very exact. They are usually just
32 bits, which means 24 bits of precision, which is a bit less than 8
decimal digits.
istr >> f; assert( std::fabs( f - 3.1415 ) < 1e-7 );
The last thing we want to demonstrate with regards to the formatted
input operators is that we can chain them. The values are taken from
left to right (behind the scenes, this is achieved by the formatted input
operator returning a reference to its left operand.
istr >> s >> t;
assert( s == "s" && t == "t" );
When we reach the end of the stream (i.e. the end of the buffer, or of
the file), the stream will indicate an error. A stream in error condition
converts to false in a bool context.
assert( !( istr >> s ) );
}
Output is actually quite a bit simpler than input. It is almost always
reasonable to use formatted output, since strings are simply copied to
the output without alterations.
void formatted_output()
{
std::ostringstream a, b, c;
a << "hello world";
To read the buffer associated with an output string stream, we use its
method str. Of course, this method is not available on other stream
types: in those cases, the characters are written to files or to the terminal
and we cannot access them through the stream anymore.
assert( a.str() == "hello world" );
Like with formatted input, output can be chained.
b << 123 << " " << 3.1415;
assert( b.str() == "123 3.1415" );
When writing delimited values to an output stream, it is often desirable
to only put the delimiter between items and not after each item: this
is an endless source of headaches. Here is a trick to do it without too
much typing:
int i = 0;
for ( int v : { 1, 2, 3 } )
c << ( i++ ? ", " : "" ) << v;
assert( c.str() == "1, 2, 3" );
}
5.d.7 [format] We have seen the basics of input and output, and that
formatted input and output is realized using operators. Like many
PB161 Programming in C++ 33/114 June 28, 2022
other operators in C++, those operators can be overloaded. We will
show how that works in this example.
We will revisit the cartesian class from last week, to represent complex
numbers in algebraic form, i.e. as a sum of a real and an imaginary
number. We do not care about arithmetic this time: we will only
implement a constructor and the formatted input and output operators.
We will, however, need equality so that we can write test cases.
class cartesian
{
double real, imag;
public:
We have seen default arguments before: those are used when no
value is supplied by the caller. This also allows instances to be default-
constructed.
cartesian( double r = 0, double i = 0 ) : real( r ), imag( i )
{}
The comparison is fuzzy, due to the limited precision available in dou-
ble.
friend bool operator==( cartesian a, cartesian b )
{
return std::fabs( a.real - b.real ) < 1e-10 &&
std::fabs( a.imag - b.imag ) < 1e-10;
}
Now the formatted output, which is a little easier than the input. Since
the first operand of this operator is not an instance of cartesian, the
operator cannot be implemented as a method. It must either be a
function outside the class, or use the ‘friend trick’. Since we will need to
access private attributes in the operator, we will use the friend syntax
here. The return type and the type of the first argument are pretty
much given and are always the same. You could consider them part
of the syntax. The second argument is an instance of our class (this
would often be passed as a const reference).
friend std::ostream &operator<<( std::ostream &o, cartesian c )
{
We will use 27.3±7.1*i as the output format. We can use ‘simpler’
overloads of the << operator to build up ours: this is a fairly common
practice. We write to the ostream instance given to us in the argument.
We must not forget to return that instance to our caller.
o << c.real;
if ( c.imag >= 0 )
o << "+";
return o << c.imag << "*i";
}
The input operator is similar. It gets a reference to an std::istream as
an argument (and has to pass it along in the return value). The main
difference is that the object into which we read the data must be passed
as a non-constant (i.e. mutable) reference, since we need to change it.
friend std::istream &operator>>( std::istream &i, cartesian &c )
{
Like above, we will build up our implementation from simpler overloads
of the same operator (which all come from the standard library).
The formatted input operators for numbers do not require that the
number is followed by whitespace, but will stop at a character which
can no longer be part of the number. A + or - character in the middle
of the number qualifies.
i >> c.real;
We will slightly abuse the flexibility of the formatted input operator for
double values: it accepts numbers starting with an explicit + sign, hence
we do not need to check the sign ourselves. Just read the imaginary
part.
i >> c.imag;
We do need to deal with the trailing *i though.
char ch;
When formatted input fails, it should set a failbit in the input stream.
This is how the if ( stream >> value ) construct works.
if ( !( i >> ch ) || ch != '*' ||
!( i >> ch ) || ch != 'i' )
i.setstate( i.failbit );
And as mentioned above, we need to return a reference to the input
stream.
return i;
}
};
int main() /* demo */
{
std::ostringstream ostr;
ostr << cartesian( 1, 1 );
We first check that the output behaves as we expected.
assert( ostr.str() == "1+1*i" );
We write a few more complex numbers into the stream, using operator
chaining.
ostr << " " << cartesian( 3, 0 ) << " " << cartesian( 1, -1 )
<< " " << cartesian( 0, 0 );
assert( ostr.str() == "1+1*i 3+0*i 1-1*i 0+0*i" );
We now construct an input stream from the string which we created
above, and check that the values can be read back.
std::istringstream istr( ostr.str() );
cartesian a, b, c;
Let’s read back the first number and check that the result makes sense.
assert( istr >> a );
assert( a == cartesian( 1, 1 ) );
We can also check that chaining works as expected, using the remaining
numbers in the string.
assert( istr >> a >> b >> c );
assert( a == cartesian( 3, 0 ) );
assert( b == cartesian( 1, -1 ) );
assert( c == cartesian( 0, 0 ) );
We can reset an istringstream by calling its str method with a new
buffer. We want to demonstrate that trying to read an ill-formatted
complex number will fail.
std::istringstream bad1( "7+3*j" );
assert( !( bad1 >> a ) );
std::istringstream bad2( "7" );
assert( !( bad2 >> a ) );
}
Part 5.e: Elementary Exercises
5.e.1 [cartesian] In this exercise, we will implement complex numbers
PB161 Programming in C++ 34/114 June 28, 2022
with addition, subtraction, unary minus and equality.
The class should be called complex (do not mind the syntax highlight).
The constructor should take 2 real numbers (the real and imaginary
parts).
class complex;
5.e.2 [force] In this example, we will define a class that represents a
(physical) force in 3D. Forces are vectors (in the mathematical sense):
they can be added and multiplied by scalars (scalars are, in this case,
real numbers). Forces can also be compared for equality (we will use
fuzzy comparison because floating point computations are inexact).
Hint: It may be useful to know that when overloading binary operators,
the operands do not need to be of the same type.
class force;
5.e.3 [forcefmt] This week in the physics department, we will deal
with formatting and parsing vectors (forces, just to avoid confusion
with std::vector... for now).
The class will be called force, and it should have a constructor which
takes 3 values of type double and a default constructor which constructs
a 0 vector. In addition to that, it should have a (fuzzy) comparison
operator and formatting operators, both for input and for output.
Use the following format: [F_x F_y F_z], that is, a left square bracket,
then the three components of the force separated by spaces, and a
closing square bracket. Do not forget to set failbit in the input stream
if the format does not match expectations.
class force;
Part 5.p: Preparatory Exercises
5.p.1 [polar] The first thing we will do is implement a simple class
which represents complex numbers using their polar form. This form
makes multiplication and division easier, so that is what we will do
here (see also cartesian.cpp for definition of addition).
• the constructor takes the modulus and the argument (angle)
• add abs and arg methods to access the attributes
• implement multiplication and division on polar
• implement equality for polar; keep in mind that if the modulus is
zero, the argument (angle) is irrelevant
NB. The argument is periodic: either normalize it to fall within [0,
2π), or otherwise make sure that polar( 1, x ) == polar( 1, x + 2π ).
The equality operator you implement should be tolerant of imprecision:
use std::fabs( x - y ) < 1e-10 instead of x == y when dealing with
real numbers.
class polar; /* reference implementation: 29 lines */
5.p.2 [rational] In this exercise, we will represent rational numbers
(fractions) with addition and ordering. The constructor of rat should
take the numerator and the denominator (in this order), which are both
integers. It should be possible to compare rat instances for equality
and inequality (in this exercise, it is enough to implement the less-than
operator , i.e. a < b).
NB. Recall how fractions with different denominators are compared
(and added). Your implementation does not need to be very efficient,
or work for very large numbers.
class rat; /* reference implementation: 9 lines */
5.p.3 [tmpfile] We will implement a simple wrapper around
std::fstream that will act as a temporary file. When the object is
destroyed, use std::remove to unlink the file. Make sure the stream is
closed before you unlink the file.
The tmpfile class should have the following interface:
• a constructor which takes the name of the file
• method write which takes a string and replaces the content of the
file with that string; this method should flush the data to the operating
system (e.g. by closing the stream)
• method read which returns the current content of the file
• method stream which returns a reference to an instance of
std::fstream (i.e. suitable for both reading and writing)
Calling both stream and write on the same object is undefined behaviour.
The read method should return all data sent to the file, including
data written to stream() that was not yet flushed by the user.
class tmpfile;
5.p.4 [nibble] In this exercise, we will implement a class that represents
an array of nibbles (half-bytes) stored compactly, using a byte
vector as backing storage. We will need 3 classes: one to represent
reference-like objects: nibble_ref, another for pointer-like objects: nibble_ptr
and finally the container to hold the nibbles: nibble_vec. NB.
In this exercise, we will not consider const-ness of values stored in the
vector.6
The nibble_ref class needs to remember a reference or a pointer to the
byte which contains the nibble that we refer to, and whether it is the
upper or the lower nibble. With that information (which should be
passed to it via a constructor), it needs to provide:
• an assignment operator which takes an uint8_t as an argument,
but only uses the lower half of that argument to overwrite the
pointed-to nibble,
• a conversion operator which allows implicit conversion of a nibble_ref
to an uint8_t.
class nibble_ref; /* reference implementation: 17 lines */
The nibble_ptr class works as a pointer. Dereferencing a nibble_ptr
should result in a nibble_ref. There is no indirect access, because the
target (pointed-to) type does not have any fields. To make nibble_ptr
more useful, it should also have:
• a pre-increment operator, which shifts the pointer to the next nibble
in memory. That is, if it points at a lower nibble, after ++x, it should
point to an upper half of the same byte, and after another ++x, it
should point to the lower half of the next byte,
• an equality comparison operator, which checks whether two nibble_ptr
instances point to the same place in memory.
class nibble_ptr; /* reference implementation: 18 lines */
And finally the nibble_vec: this class should provide 4 methods:
• push_back, which adds a nibble at the end,
• begin, which returns a nibble_ptr to the first stored nibble (lower
half of the first byte),
• end, which returns a nibble_ptr past the last stored nibble (i.e. the
first nibble that is not in the container), and finally
• indexing operator, which returns a nibble_ref.
class nibble_vec; /* reference implementation: 16 lines */
5.p.5 [grep] To practice working with IO streams a little, we will write
a two simple functions which reads lines from an input stream, process
them a little and possibly print them out or their part into an output
stream.
6
In particular, obtaining a pointer (e.g. by using begin) will allow you to change the value that
it points to, even if the vector itself was marked const. We will deal with this issue properly
toward the end of the semester.
PB161 Programming in C++ 35/114 June 28, 2022
The grep function checks, for every line on the input, whether it
matches a given pattern (i.e. the pattern is a substring of the line)
and if it does (and only if it does) copies the line to the output stream.
void grep( std::string pattern, std::istream &, std::ostream & );
The other function to add is called cut and it will process the lines
differently: it splits each line into fields separated by the character
delim and only prints the column given by col. Unlike the cut program,
index columns starting at 0. If there are not enough columns on a
given line, print an empty line.
void cut( char delim, int col, std::istream &, std::ostream & );
5.p.6 [fixnum] In this exercise, we will implement fixed-precision numbers,
with 2 fractional digits and up to 6 integral digits (both decimal),
i.e. numbers of the form ‘123456.78’.
This is the class which we will use for indicating that parsing of the
fixnum has failed (i.e. this class will be thrown as an exception in that
case).
class bad_format;
The fixnum class should provide following operations: addition, subtraction
and multiplication. It should have explicit constructors which
construct the number from an integer or from a string. The latter
constructor should throw an exception if the string is ill-formed (it is
okay to only handle positive numbers in string form). Finally, it should
be possible to compare fixnum instances for equality. All operations
should round toward zero, to the nearest representable number.
class fixnum; /* reference implementation: 32 lines */
Part 5.r: Regular Exercises
5.r.1 [poly] Goal: implement polynomials with addition (easy) and multiplication
(less easy). A polynomial is a term of the form 7x4
+ 0x3
+
0x2
+ 3x + x0
– i.e. a sum of non-negative integral powers of x, with
each power carrying a fixed (constant) coefficient. Adding two polynomials
will simply give us a polynomial where coefficients are sums of
the coefficients of the two addends. The case of multiplication is more
complicated, because:
• each term of the first polynomial has to be multiplied by each term
of the second polynomial
• some of those products give equal powers of x and hence their
coefficients need to be summed
For each polynomial, there is some n, such that all powers higher than
n have a zero coefficient. This is important when you want to store
the polynomials in a computer.
The default constructor of the class poly should generate a polynomial
which has all coefficients set to 0. Besides addition and multiplication
(which are implemented as operators), also implement equality and a
method set, which takes an exponent (power of x) and a coefficient,
both integers.
class poly; /* reference implementation is 45 lines */
5.r.2 [csv] In this exercise, we will deal with CSV files: we will implement
a class called csv which will read data from an input stream and
allow the user to access it using the indexing operator.
The exception to throw in case of format error.
class bad_format;
The constructor should accept a reference to std::istream and the
expected number of columns. In the input, each line contains integers
separated by value. The constructor should throw an instance of
bad_format if the number of columns does not match.
Additionally, if x is an instance of csv, then x[ 3 ][ 1 ] should return
the value in the third row and first column.
class csv;
5.r.3 [set] In this exercise, we will implement a set of arbitrary integers,
with the following operations: union using |, intersection using
&, difference using - and inclusion using <=. Use efficient algorithms
for the operations (check out what’s available in the standard header
algorithm). Provide methods add and has to add elements and test their
presence.
class set; /* reference implementation: 36 lines */
5.r.4 [json] You are given a single-level string → string dictionary.
Turn it into a single string, using JSON as the format. Take care to escape
special characters – at least double quote and the escape character
(backslash) itself.
In JSON, key order is not important – emit them in iteration (alphabetic)
order. Put a single space after each ‘element’: after the opening brace,
after colons and after commas, except if the input is empty, in which
case the output should be just {}.
using str_dict = std::map< std::string, std::string >;
std::string to_json( const str_dict &dict );
5.r.5 [cpp] Implement a (very simplified) C preprocessor which supports
#include "foo" (without a search path, working directory only),
#define without a value, #undef, #ifdef and #endif. The input is provided
in a file, but the output should be returned as a string.
PS: Do not include line and filename information that cpp normally
adds to files.
std::string cpp( const std::string &filename );
If you run this program with a parameter, it’ll preprocess that file and
print the result to stdout. Feel free to experiment.
int main( int argc, const char **argv )
{
if ( argc >= 2 )
std::cout << cpp( argv[ 1 ] );
else
{
std::string actual_1 = cpp( "zz.preproc_1.txt" ),
expect_1 = "included foo\n"
"included bar\n"
"xoo\n"
"foo\n",
actual_2 = cpp( "zz.preproc_2.txt" ),
expect_2 = "included bar\n"
"included baz\n"
"included bar\n";
assert( actual_1 == expect_1 );
assert( actual_2 == expect_2 );
}
return 0;
}
PB161 Programming in C++ 36/114 June 28, 2022
Part 6: Exceptions and RAII
Demonstrations:
1. exceptions – throwing and catching exceptions
2. stdexcept – the standard exception hierarchy
3. semaphore – automatic management of finite resources
4. swarm – keeping the swarm under control
Elementary exercises:
1. default – read a number or return a default value
2. counter – count the number of instances of a class
3. coffee – a simple model of a coffee machine
Preparatory exercises:
1. fd – POSIX file descriptors
2. loan – database-style transactions with resources
3. library – borrowing books
4. parse – a simple parser which throws exceptions
5. invest – we further stretch the banking story
6. linear – linear equations, with some exceptions
Regular exercises:
1. printing – printing with a monthly budget
2. bsearch – a key-value vector which throws on failure
3. enzyme – cellular chemistry with RAII
4. tinyvec † – a vector in a fixed memory buffer
5. lock – a movable mutual exclusion token
6. bounded – a bounded queue that throws when full
Part 6.d: Demonstrations
6.d.1 [exceptions] Exceptions are, as their name suggests, a mechanism
for handling unexpected or otherwise exceptional circumstances,
typically error conditions. A canonic example would be trying to open
a file which does not exist, trying to allocate memory when there is
no free memory left and the like. Another common circumstance
would be errors during processing user input: bad format, unexpected
switches and so on.
NB. Do not use exceptions for ‘normal’ control flow, e.g. for terminating
loops. That is a really bad idea (even though try blocks are cheap,
throwing exceptions is very expensive).
This example will be somewhat banal. We start by creating a class
which has a global counter of instances attached to it: i.e. the value of
counter tells us how many instances of counted exist at any given time.
Fair warning, do not do this at home.
int counter = 0;
struct counted
{
counted() { ++ counter; }
~counted() { -- counter; }
};
A few functions which throw exceptions and/or create instances of
the counted class above. Notice that a throw statement immediately
stops the execution and propagates up the call stack until it hits a try
block (shown in the main function below). The same applies to a function
call which hits an exception: the calling function is interrupted
immediately.
int f() { counted x; return 7; }
int g() { counted x; throw std::bad_alloc(); assert( 0 ); }
int h() { throw std::runtime_error( "h" ); }
int i() { counted x; g(); assert( 0 ); }
int main() /* demo */
{
bool caught = false;
A try block allows us to detect that an exception was thrown and react,
based on the type and attributes of the exception. Otherwise, it is a
regular block with associated scope, and behaves normally.
try
{
counted x;
assert( counter == 1 );
f();
assert( counter == 1 );
}
One or more catch blocks can be attached to a try block: those describe
what to do in case an exception of a matching type is thrown in one
of the statements of the try block. The catch clause behaves like a
prototype of a single-argument function – if it could be ‘called’ with
the thrown exception as an argument, it is executed to handle the
exception.
This particular catch block is never executed, because nothing in the
associated try block above throws a matching exception (or rather, any
exception at all):
catch ( const std::bad_alloc & ) { assert( false ); }
The counted instance x above went out of scope:
assert( counter == 0 );
Let’s write another try block. This time, the i call in the try block
throws, indirectly (via g) an exception of type std::bad_alloc.
try { i(); }
To demonstrate how catch blocks are selected, we will first add one
for std::runtime_error, which will not trigger (the ‘prototype’ does not
match the exception type that was thrown):
catch ( const std::runtime_error & ) { assert( false ); }
As mentioned above, each try block can have multiple catch blocks, so
let’s add another one, this time for the bad_alloc that is actually thrown.
If the catch matches the exception type, it is executed and propagation
of the exception is stopped: it is now handled and execution continues
normally after the end of the catch sequence.
catch ( const std::bad_alloc & ) { caught = true; }
Execution continues here. We check that the catch block was actually
executed:
assert( caught );
assert( counter == 0 ); // no ‹counted› instances were leaked
}
6.d.2 [stdexcept] It is possible to sub-class standard exception classes.
For most uses, std::runtime_error is the most appropriate base class.
class custom_exception : public std::runtime_error
{
public:
custom_exception() : std::runtime_error( "custom" ) {}
};
This demo simply demonstrates some of the standard exception types
(i.e. those that are part of the standard library, and which are thrown
by standard functions or methods; as long as those methods or functions
are not too arcane).
PB161 Programming in C++ 37/114 June 28, 2022
int main() /* demo */
{
try
{
throw custom_exception();
assert( false );
}
As per standard rules, it’s possible to catch exceptions of derived classes
(of course including user-defined types) via a catch clause which accepts
a reference to a superclass.
catch ( const std::exception & ) {}
try
{
std::vector x{ 1, 2 };
Attempting out-of-bounds access through at gives std::out_of_range
x.at( 7 );
assert( false );
}
catch ( const std::out_of_range & ) {}
try
{
If the string passed to stoi is not a number, we get back an exception
of type std::invalid_argument.
std::stoi( "foo" );
assert( false );
}
catch ( const std::invalid_argument & ) {}
try
{
If an integer is too big to fit the result type, stoi throws
std::out_of_range.
std::stoi( "123456123456123456" );
assert( false );
}
catch ( const std::out_of_range & ) {}
try
{
System-interfacing functions may throw std::system_error. Here, for
instance, trying to detach a thread which was not started.
std::thread().detach();
assert( false );
}
catch ( const std::system_error & ) {}
try
{
Throwing a system_error is the appropriate reaction when dealing with
a failure of a POSIX function which sets errno.
int fd = ::open( "/does/not/exist", O_RDONLY );
if ( fd < 0 )
throw std::system_error( errno, std::system_category(),
"opening /does/not/exist" );
assert( false );
}
catch ( const std::system_error & ) {}
try
{
Passing a size that is more than max_size() when constructing or resizing
an std::string or an std::vector gives us back an std::length_error.
Note that the -1 turns into a really big number in this context.
std::string x( -1, 'x' );
assert( false );
}
catch ( const std::length_error & ) {}
try
{
std::bitset< 128 > x;
x[ 100 ] = true;
Trying to convert an std::bitset to an integer type may throw
std::overflow_error, if there are bits set that do not fit into the target
integer type.
x.to_ulong();
assert( false );
}
catch ( const std::overflow_error & ) {}
}
6.d.3 [semaphore] In this demo, we will implement a simple semaphore.
A semaphore is a device which guards a resource of which there are
multiple instances, but the number of instances is limited. It is a slight
generalization of a mutex (which guards a singleton resource). Internally,
semaphore simply counts the number of clients who hold the
resource and refuses further requests if the maximum is reached. In a
multi-threaded program, semaphores would typically block (wait for
a slot to become available) instead of refusing. In a single-threaded
program (which is what we are going to use for a demonstration), this
would not work. Hence our get method returns a bool, indicating
whether acquisition of the lock succeeded.
class semaphore
{
int _available;
public:
When a semaphore is constructed, we need to know how many instances
of the resource are available.
explicit semaphore( int max ) : _available( max ) {}
Classes which represent resource managers (in this case ‘things that
can be locked’ as opposed to ‘locks held’) have some tough choices
to make. If they are impossible to copy/move/assign, users will find
that they must not appear as attributes in their classes, lest those too
become un-copyable (and un-movable) by default. However, this is
how the standard library deals with the problem, see std::mutex or
std::condition_variable. While it is the safest option, it is also the
most annoying. Nonetheless, we will do the same.
semaphore( const semaphore & ) = delete;
semaphore &operator=( const semaphore & ) = delete;
We allow would-be lock holders to query the number of resource instances
currently available. Perhaps if none are left, they can make
do without one, or they can perform some other activity in the hopes
that the resource becomes available later.
int available() const
{
return _available;
}
Finally, what follows is the ‘low-level’ interface to the semaphore. It
is completely unsafe, and it is inadvisable to use it directly, other than
perhaps in special circumstances. This being C++, such interfaces are
commonly made available. Again see std::mutex for an example.
PB161 Programming in C++ 38/114 June 28, 2022
However, it would also be an option to be strict about it, make the
following 2 methods private, and declare the RAII class defined below,
semaphore_lock, to be a friend of this one.
bool get()
{
if ( _available > 0 )
return _available --;
else
return false;
}
void put()
{
++ _available;
}
};
We will want to write a RAII ‘lock holder’ class. However, since get
above might fail, we need a way to indicate the failure in the RAII
class as well. But constructors don’t return values: it is therefore a
reasonable choice to throw an exception. It is reasonable as long as we
don’t expect the failure to be a common scenario.
class resource_exhausted : public std::runtime_error
{
public:
resource_exhausted()
: std::runtime_error( "semaphore full" )
{}
};
Now the RAII class itself. It will need to hold a reference to the semaphore
for which it holds a lock (good thing the semaphore is not
movable, so we don’t have to think about its address changing). Of
course, it must not be possible to make a copy of the resource class: we
cannot duplicate the resource, which is a lock being held. However,
it does make sense to move the lock to a new owner, if the client so
wishes. Hence, both a move constructor and move assignment are
appropriate.
class semaphore_lock
{
semaphore *_sem = nullptr;
public:
To construct a semaphore lock, we understandably need a reference to
the semaphore which we wish to lock. You might be wondering why
the attribute is a pointer and the argument is a reference. The main
difference between references and pointers (except the syntactic sugar)
is that references cannot be null. In a correct program, all references
always refer to valid objects. It does not make sense to construct a
semaphore_lock which does not lock anything. Hence the reference.
Why the pointer in the attributes? That will become clear shortly.
Before we move on, notice that, as promised, we throw an exception if
the locking fails. Hence, no noexcept on this constructor.
semaphore_lock( semaphore &s ) : _sem( &s )
{
if ( !_sem->get() )
throw resource_exhausted();
}
As outlined above, semaphore locks cannot be copied or assigned. Let’s
make that explicit.
semaphore_lock( const semaphore_lock & ) = delete;
semaphore_lock &operator=( const semaphore_lock & ) = delete;
The new object (the one initialized by the move constructor) is quite
unremarkable. The interesting part is what happens to the ‘old’ (source)
instance: we need to make sure that when it is destroyed, it does not
release the resource (i.e. the lock held) – the ownership of that has been
transferred to the new instance. This is where the pointer comes in
handy: we can assign nullptr to the pointer held by the source instance.
Then we just need to be careful when we release the resource (in the
destructor, but also in the move assignment operator) – we must first
check whether the pointer is valid.
Also notice the noexcept qualifier: even though the ‘normal’ constructor
throws, we are not trying to obtain a new resource here, and there is
nothing in the constructor that might fail. This is good, because move
constructors, as a general rule, should not throw.
semaphore_lock( semaphore_lock &&src ) noexcept
: _sem( src._sem )
{
src._sem = nullptr;
}
We now define a helper method, release, which frees up (releases) the
resource held by this instance. It will do this by calling put on the
semaphore. However, if the semaphore is null, we do nothing: the
instance has been moved from, and no longer owns any resources.
Why the helper method? Two reasons:
1. it will be useful in both the move assignment operator and in the
destructor,
2. the client might need to release the resource before the instance
goes out of scope or is otherwise destroyed ‘naturally’ (compare
std::fstream::close()).
void release() noexcept
{
if ( _sem )
_sem->put();
}
Armed with release, writing both the move assignment and the destructor
is easy. The move assignment is also noexcept, which is
semaphore_lock &operator=( semaphore_lock &&src ) noexcept
{
First release the resource held by the current instance. We cannot
hold both the old and the new resource at the same time.
release();
Now we reset our _sem pointer and update the src instance – the resource
is now in our ownership.
_sem = src._sem;
src._sem = nullptr;
return *this;
}
~semaphore_lock() noexcept
{
release();
}
};
int main() /* demo */
{
semaphore sem( 3 );
sem.get();
semaphore_lock l1( sem );
bool l4_made = false;
try
{
semaphore_lock l2( sem );
assert( sem.available() == 0 );
PB161 Programming in C++ 39/114 June 28, 2022
semaphore_lock l3 = std::move( l2 );
assert( sem.available() == 0 );
semaphore_lock l4 = std::move( l1 );
assert( sem.available() == 0 );
l4_made = true;
semaphore_lock l5( sem );
assert( false );
}
catch ( const resource_exhausted & ) {}
assert( l4_made );
assert( sem.available() == 2 );
// clang-tidy: -clang-analyzer-deadcode.DeadStores
}
6.d.4 [swarm] TBD. Create overlords which create a resource and nonoverlords
which consume it. Enforce the balance by throwing an
exception on exhaustion.
class swarm;
class unit
{
swarm &owner;
};
class overlord : unit
{
};
class zergling : unit
{
};
class swarm
{
int _control = 3;
int _resource = 200;
public:
overlord spawn_overlord();
zergling spawn_zergling();
};
int main() /* demo */
{
swarm s;
std::vector< zergling > zerglings;
std::vector< overlord > overlords;
zerglings.emplace_back( s );
}
Part 6.e: Elementary Exercises
6.e.1 [default] Write a function stoi_or which takes a string and an
int. If the string can be parsed using std::stoi, return the result of
stoi, otherwise return the ‘default’ value from the second argument.
6.e.2 [counter]
static int counter = 0;
Add constructors and a destructor to counted in such a way that counter
above always corresponds to the number of instances of counted that
exist at any given time.
struct counted;
6.e.3 [coffee] Implement a coffee machine which gives out a token
when the order is placed and takes the token back when it is done… at
most one order can be in progress.
Throw this when the machine is already busy making coffee.
class busy {};
And this when trying to use a default-constructed or already-used
token.
class invalid {};
Fill in the two classes. Besides constructors and assignment operators,
add methods make and fetch to machine, to create and redeem tokens
respectively.
class machine;
class token;
6.e.4 [lock] TBD lock a resource, with ownership transfer but no copy
Part 6.p: Preparatory Exercises
6.p.1 [fd] In POSIX systems, opening a file or a file-like resource gives
us a file descriptor, a small number that can be passed to system calls
such as read or write. The descriptor must be closed when it is no
longer needed, by calling close on it exactly once (it is important not
to close the same descriptor twice). Write a class which safely wraps a
file descriptor so that we can’t accidentally lose it or close it twice.
It should be possible to move-construct and move-assign file descriptors.
A new valid descriptor can be created in 2 ways: by calling
fd::open( "file", flags ) or fd::dup( raw_fd ) where flags and
raw_fd are both int. Use POSIX functions open and dup to implement
this. Run man 2 open and man 2 dup on aisa for details about these
POSIX functions.
Add methods read and write to the fd class, the first will simply take an
integer, read the given number of bytes and return an std::string. The
latter will take an std::string and write it into the descriptor. Again
see man 2 read and man 2 write on aisa for advice.
If open, read or write fails, throw std::system_error. Attempting to call
read or write on an invalid descriptor (one that was default-constructed
or already closed) should throw std::invalid_argument.
6.p.2 [loan] Let us revisit the bank account story from first week. We
will have 2 classes this time: an account, which has the usual methods:
deposit, withdraw, balance; to simplify things, we will only add a default
constructor, which sets the initial balance to 0.
The other class will be called loan, and its constructor will take a reference
to an account and the amount loaned (an int). Constructing a
loan object will deposit the loaned amount to the referenced account.
It will also have a method called repay which takes an integer, which
withdraws the given amount from the associated account and reduces
the amount owed by the same sum. Attempting to repay more than is
owed should throw std::out_of_range.
Make sure that we can’t accidentally destroy a loan without repaying
it first. Does it make sense to make a copy of a loan? How about move?
And assignment?
class account;
class loan;
6.p.3 [library] A very simple library model: patrons can borrow books
and borrowed books can be moved around, and must be eventually
returned. The library should have the following methods:
• add_book, which creates a book record based on 2 arguments – the
title (a string) and the number of copies (an integer) of the book –
and returns a suitable object (a handle) to represent that book,
• add_patron which creates a patron, given a name (a string), and again
returns a suitable object to represent the patron.
It should be possible to call borrow on objects which represent patrons,
PB161 Programming in C++ 40/114 June 28, 2022
passing either a reference to a library or another patron as the first
argument, and the book handle as a second argument. It returns true
if the borrowing was a success, or false otherwise (no copies were
available). If a patron is destroyed, all books in their possession return
to the library. Destroying a book handle does nothing.
class library;
Finally, the class loan holds information about a loan. Both library
and the patron object get a method give which returns a loan object
associated with the book passed to it, and take, which accepts a loan
object and takes ownership of the associated book. If give is called on
an object which does not have a copy of the requested book, return an
invalid (empty) loan object.
While a book is held in a loan instance, it is not in the possession of
any of the objects, but it is checked out from the library. If the loan
object is destroyed without being taken by anyone, the book returns
to the library.
class loan;
6.p.4 [parse] Write a simple parser for an assembly-like language with
one instruction per line (each taking 2 operands, separated by spaces,
where the first is always a register and the second is either a register
or an ‘immediate’ number).
The opcodes (instructions) are: add, mul, jnz, the registers are rax, rbx
and rcx. The result is a vector of instruction instances (see below). Set
r_2 to reg::immediate if the second operand is a number.
If the input does not conform to the expected format, throw no_parse,
which includes a line number with the first erroneous instruction and
the kind of error (see enum error), as public attributes line and type,
respectively. If multiple errors appear on the same line, give the one
that comes first in the definition of error. You can add attributes or
methods to the structures below, but do not change the enumerations.
enum class opcode { add, mul, jnz };
enum class reg { rax, rbx, rcx, immediate };
enum class error { bad_opcode, bad_register, bad_immediate,
bad_structure };
struct instruction
{
opcode op;
reg r_1, r_2;
int32_t immediate;
};
struct no_parse
{
int line;
error type;
};
std::vector< instruction > parse( const std::string & );
#include <iostream>
6.p.5 [invest] We will revisit (again) our familiar example of a bank
account. This time, we add exceptions to the story: withdrawals that
would exceed the overdraft limit will throw. We will also add a class
dual to loan from the last time: an investment, which will deduct money
from an account upon construction, accrue interest, and upon destruction,
deposit the money into the original account.
We will use this class as the exception type. It is okay to keep it empty.
class insufficient_funds;
First the account class, which has the usual methods: balance, deposit
and withdraw. The starting balance is 0. The balance must be nonnegative
at all times: an attempt to withdraw more money than available
should throw an exception of type insufficient_funds.
class account; /* reference implementation: 13 lines */
And finally the class investment, which has a three-parameter constructor:
it takes a reference to an account, the sum to invest and a yearly
interest rate (in percent, as an integer). Upon construction, it must
withdraw the sum from the account, and upon destruction, deposit
the original sum plus the interest. The method next_year should update
the accrued interest.
class investment; /* reference implementation: 15 lines */
6.p.6 [linear] Write a solver for linear equations in 2 variables. The
interface will be a little unconventional: overload operators +, * and
== and define global constants x and y of suitable types, so that it is
possible to write the equations as shown in main below.
Note that the return type of == does not have to be bool. It can be
any type you like, including of course custom types. For solve, I would
suggest looking up Cramer’s rule.
ref: class eqn 25 lines, solve 8 lines, x and y 2 lines
If the system has no solution, throw an exception of type no_solution.
Derive it from std::exception.
Part 6.r: Regular Exercises
6.r.1 [printing] Jobs need resources (printing credits, where 1 page
= 1 credit) which must be reserved when the job is queued, but are
only consumed at actual printing time; jobs can be moved between
queues (printers) by the system, and jobs that are still in the queue can
be aborted.
The class job represents a document to be printed, along with resources
that have already been earmarked for its printing.
• The constructor should take a numeric identifier, the name of the
user who owns the job, and the number of pages (= credits allocated
for the job),
• method owner should return the name of the owner,
• method page_count should return the number of pages.
class job;
A single queue instance represents a printer. It should have the following
methods:
• dequeue: consume (print) the oldest job in the queue and return its
id,
• enqueue: add a job to the queue,
• release( id ): remove the job given by id from the queue and return
it to the caller,
• page_count: number of pages in the queue.
You can assume that oldest job has the lowest id.
class queue;
class insufficient_credit {};
class print_sys
{
int _last_id = 0;
std::vector< queue > _printers;
std::map< std::string, int > _credit;
std::map< int, int > _jobs;
public:
int print( std::string user, int pages )
{
if ( _credit[ user ] < pages )
PB161 Programming in C++ 41/114 June 28, 2022
throw insufficient_credit();
assert( !_printers.empty() );
int qid = 0;
for ( size_t i = 0; i < _printers.size(); ++i )
if ( _printers[ i ].page_count() < _printers[ qid
].page_count() )
qid = i;
int jid = _last_id ++;
_printers[ qid ].enqueue( job( jid, user, pages ) );
_jobs[ jid ] = qid;
_credit[ user ] -= pages;
return jid;
}
bool abort( int jid )
{
if ( !_jobs.count( jid ) )
return false;
auto &queue = _printers[ _jobs[ jid ] ];
job j = queue.release( jid );
_credit[ j.owner() ] += j.page_count();
_jobs.erase( jid );
return true;
}
int add_printer()
{
_printers.emplace_back();
return int( _printers.size() ) - 1;
}
void add_credit( std::string user, int n )
{
_credit[ user ] += n;
}
void printing_done( int qid )
{
if ( _printers[ qid ].page_count() > 0 )
{
int id = _printers[ qid ].dequeue();
assert( _jobs.count( id ) );
assert( _jobs[ id ] == qid );
_jobs.erase( id );
}
}
};
6.r.2 [bsearch] Let’s revisit the perennial favourite: binary search. We
will implement a container similar to std::map. Let’s assume that it’ll
be used in a search-heavy scenario, so the cost of insertion is much
less important than the cost of lookup. A good candidate, then, would
be a sorted vector (lookup is logarithmic like with a tree, but the data
is stored much more compactly).
Implement at least emplace, an indexing operator, and at, with semantics
familiar from std::map, except emplace should simply return a bool
(we will not write iterators).
Finally, since we still don’t know how to write generic classes, use
strings for keys and token instances for values.
class token
{
int _value;
public:
token( int i ) : _value( i ) {}
token( const token & ) = delete;
token &operator=( const token & ) = delete;
token( token && ) = default;
token &operator=( token && ) = default;
token &operator=( int v ) { _value = v; return *this; }
bool operator==( int v ) const { return _value == v; }
};
class flat_map;
6.r.3 [enzyme] TBD. Reactions tie up enzymes, which return to the pool
after the reaction is done. Different reactions need different sets of
enzymes present, and a given enzyme cannot be used by more than
one reaction at a time.
6.r.4 [tinyvec] † Implement tiny_vector, a class which works like a
vector, but instead of allocating memory dynamically, it uses a fixedsize
buffer (32 bytes) which is part of the object itself (use e.g. an
std::array of bytes). Like earlier, we will use token as the value type.
Provide the following methods:
• insert (take an index and an rvalue reference),
• erase (take an index),
• back and front, with appropriate return types.
In this exercise (unlike in most others), you are allowed to use reinter-
pret_cast.
class token
{
int _value;
bool _robbed = false;
public:
static int _count;
token( int i ) : _value( i ) { ++ _count; }
~token() { if ( !_robbed ) -- _count; }
token( const token & ) = delete;
token( token &&o ) : _value( o._value ) { o._robbed = true; }
token &operator=( const token & ) = delete;
token &operator=( token &&o )
{
if ( !_robbed && o._robbed ) -- _count;
_value = o._value;
_robbed = o._robbed;
o._robbed = true;
return *this;
}
token &operator=( int v )
{
_value = v;
_robbed = false;
return *this;
}
bool operator==( int v ) const
{
assert( !_robbed );
return _value == v;
}
};
Throw this if insert is attempted but the element wouldn’t fit into the
buffer.
class insufficient_space {};
Hint: Use uninitialized_* and destroy(_at) functions from the memory
header.
class tiny_vector;
int token::_count = 0;
PB161 Programming in C++ 42/114 June 28, 2022
6.r.5 [lock] Implement class lock which holds a mutex locked as long
as it exists. The lock instance can be moved around. For simplicity, the
mutex itself is immovable.
class mutex
{
bool _locked = false;
public:
~mutex() { assert( !_locked ); }
mutex() = default;
mutex( const mutex & ) = delete;
mutex( mutex && ) = delete;
mutex &operator=( const mutex & ) = delete;
mutex &operator=( mutex && ) = delete;
void lock() { assert( !_locked ); _locked = true; }
void unlock() { assert( _locked ); _locked = false; }
bool locked() const { return _locked; }
};
class lock;
6.r.6 [bounded] Implement a simple FIFO of integers. The constructor
takes the maximum number of items in the queue as its sole argument.
Add methods push, pop, full, empty and next (the last of which simply
returns the next value, without changing anything). If the queue is
full, push should throw insufficient_space.
Try to make the implementation efficient (i.e. no deque).
class insufficient_space;
class bounded_queue;
Part 7: Memory and Smart Pointers
Before you dig into the demonstrations and exercises, do not forget
to read the extended introduction below. That said, the units for this
week are, starting with demonstrations:
1. queue – a queue with stable references
2. finexp – like regexps but finite
3. expr – expressions with operators and shared pointers
4. family – genealogy with weak pointers
Elementary exercises:
1. dynarray – a simple array with a dynamic size
2. list – a simple linked list with minimal interface
Preparatory exercises:
1. unrolled – a linked list of arrays
2. bittrie – bitwise tries (radix trees)
3. solid – efficient storage of optional data
4. chartrie – binary tree for holding string keys
5. bdd – binary decision diagrams
6. rope – a string-like structure with cheap concatenation
Regular exercises:
1. circular – a singly-linked circular list
2. zipper – implementing zipper as a linked list
3. segment – a binary tree of disjoint intervals
4. diff – automatic differentiation
5. critbit – more efficient version of binary tries
6. refcnt † – implement a simple reference-counted heap
Part 7.A: Exclusive Ownership
So far, we have managed to almost entirely avoid thinking about memory
management: standard containers manage memory behind the
scenes. We sometimes had to think about copies (or rather avoiding
them), because containers could carry a lot of memory around and
copying all that memory without a good reason is rather wasteful (this
is why we often pass arguments as const references and not as values).
This week, we will look more closely at how memory management
works and what we can do when standard containers are inadequate
to deal with a given problem. In particular, we will look at building our
own pointer-based data structures and how we can retain automatic
memory management in those cases using std::unique_ptr.
XXX
Part 7.B: Shared Ownership
While unique_ptr is very useful and efficient, it only works in cases
where the ownership structure is clear, and a given object has a single
owner. When ownership of a single object is shared by multiple entities
(objects, running functions or otherwise), we cannot use unique_ptr.
To be slightly more explicit: shared ownership only arises when the
lifetime of the objects sharing ownership is not tied to each other. If
A owns B and A and B both need references to C, we can assign the
ownership of C to object A: since it also owns B, it must live at least as
long as B and hence there ownership is not actually shared.
However, if A needs to be able to transfer ownership of B to some
other, unrelated object while still retaining a reference to C, then C
will indeed be in shared ownership: either A or B may expire first, and
hence neither can safely destroy the shared instance of C to which
they both keep references. In many modern languages, this problem
is solved by a garbage collector, but alas, C++ does not have one.
Of course, it is usually better to design data structures in a way that
allows for clear, 1:1 ownership structure. Unfortunately, this is not
always easy, and sometimes it is not the most efficient solution either.
Specifically, when dealing with large immutable (or persistent, in the
functional programming sense) data structures, shared ownership can
save considerable amount of memory, without introducing any ill sideeffects,
by only storing common sub-structures once, instead of cloning
them. Of course, there are also cases where shared mutable state is
the most efficient solution to a problem.
Part 7.d: Demonstrations
7.d.1 [queue] In this example, we will demonstrate the use of
std::unique_ptr, which is an RAII class for holding (owning) values
dynamically allocated from the heap. We will implement a simple
one-way, non-indexable queue. We will require that it is possible to
erase elements from the middle in O(1), without invalidating any other
iterators. The standard containers which could fit:
• std::deque fails the erase in the middle requirement,
• std::forward_list does not directly support queue-like operation,
hence using it as a queue is possible but awkward; wrapping
std::forward_list would be, however, a viable approach to this task,
too,
• std::list works well as a queue out of the box, but has twice the
memory overhead of std::forward_list.
PB161 Programming in C++ 43/114 June 28, 2022
As usual, since we do not yet understand templates, we will only implement
a queue of integers, but it is not hard to imagine we could
generalize to any type of element.
Since we are going for a custom, node-based structure, we will need
to first define the class to represent the nodes. For sake of simplicity,
we will not encapsulate the attributes.
struct queue_node
{
We do not want to handle all the memory management ourselves. To
rule out the possibility of accidentally introducing memory leaks, we
will use std::unique_ptr to manage allocated memory for us. Whenever
a unique_ptr is destroyed, it will free up any associated memory.
An important limitation of unique_ptr is that each piece of memory
managed by a unique_ptr must have exactly one instance of unique_ptr
pointing to it. When this instance is destroyed, the memory is deallo-
cated.
std::unique_ptr< queue_node > next;
Besides the structure itself, we of course also need to store the actual
data. We will store a single integer per node.
int value;
};
We will also need to be able to iterate over the queue. For that, we
define an iterator, which is really just a slightly generalized pointer
(you may remember nibble_ptr from last week). We need 3 things:
pre-increment, dereference and inequality.
struct queue_iterator
{
queue_node *node;
The queue will need to create instances of a queue_iterator. Let’s make
that convenient.
queue_iterator( queue_node *n ) : node( n ) {}
The pre-increment operator simply shifts the pointer to the next
pointer of the currently active node.
queue_iterator &operator++()
{
node = node->next.get();
return *this;
}
Inequality is very simple (we need this because the condition of iteration
loops is it != c.end(), including range for loops):
bool operator!=( const queue_iterator &o ) const
{
return o.node != node;
}
And finally the dereference operator. This should be familiar by now
(perhaps notice the const overload). Depending on element type, the
const overload would in many cases return a const reference instead
of a value.
int &operator*() { return node->value; }
int operator*() const { return node->value; }
};
This class represents the queue itself. We will have push and pop to add
and remove items, empty to check for emptiness and begin and end to
implement iteration.
class queue
{
We will keep the head of the list in another unique_ptr. An empty
queue will be represented by a null head. Also worth noting is that
when using a list as a queue, the head is where we remove items. The
end of the queue (where we add new items) is represented by a plain
pointer because it does not own the node (the node is owned by its
predecessor).
std::unique_ptr< queue_node > first;
queue_node *last = nullptr;
public:
As mentioned above, adding new items is done at the ‘tail’ end of the
list. This is quite straightforward: we simply create the node, chain
it into the list (using the last pointer as a shortcut) and point the last
pointer at the newly appended node. We need to handle empty and
non-empty lists separately because we chose to represent an empty
list using null head, instead of using a dummy node.
void push( int v )
{
if ( last ) /* non-empty list */
{
last->next = std::make_unique< queue_node >();
last = last->next.get();
}
else /* empty list */
{
first = std::make_unique< queue_node >();
last = first.get();
}
last->value = v;
}
Reading off the value from the head is easy enough. However, to
remove the corresponding node, we need to be able to point first at
the next item in the queue.
Unfortunately, we cannot use normal assignment (because copying
unique_ptr is not allowed). We will have to use an operation that is
called move assignment and which is written using a helper function
in from the standard library, called std::move.
Operations which move their operands invalidate the moved-from
instance. In this case, first->next is the moved-from object and the
move will turn it into a null pointer. In any case, the next pointer which
was invalidated was stored in the old head node and by rewriting first,
we lost all pointers to that node. This means two things:
1. the old head’s next pointer, now null, is no longer accessible
2. memory allocated to hold the old head node is freed
int pop()
{
int v = first->value;
first = std::move( first->next );
Do not forget to update the last pointer in case we popped the last
item.
if ( !first ) last = nullptr;
return v;
}
The emptiness check is simple enough.
bool empty() const { return !last; }
Now the begin and end methods. We start iterating from the head (since
we have no choice but to iterate in the direction of the next pointers).
The end method should return a so-called past-the-end iterator, i.e.
one that comes right after the last real element in the queue. For an
empty queue, both begin and end should be the same. Conveniently,
PB161 Programming in C++ 44/114 June 28, 2022
the next pointer in the last real node is nullptr, so we can use that as
our end-of-queue sentinel quite naturally. You may want to go back
to the pre-increment operator of queue_iterator just in case.
queue_iterator begin() { return { first.get() }; }
queue_iterator end() { return { nullptr }; }
And finally, erasing elements. Since this is a singly-linked list, to erase
an element, we need an iterator to the element before the one we are
about to erase. This is not really a problem, because erasing at the head
is done by pop. We use the same move assignment construct that we
have seen in pop earlier.
void erase_after( queue_iterator i )
{
assert( i.node->next );
i.node->next = std::move( i.node->next->next );
}
};
int main() /* demo */
{
We start by constructing an (empty) queue and doing some basic operations
on it. For now, we only try to insert and remove a single
element.
queue q;
assert( q.empty() );
q.push( 7 );
assert( !q.empty() );
assert( q.pop() == 7 );
assert( q.empty() );
Now that we have emptied the queue again, we add a few more items
and try erasing one and iterating over the rest.
q.push( 1 );
q.push( 2 );
q.push( 7 );
q.push( 3 );
We check that erase works as expected. We get an iterator that points
to the value 2 from above and use it to erase the value 7.
queue_iterator i = q.begin();
++ i;
assert( *i == 2 );
q.erase_after( i );
We can use instances of queue in range for loops, because they have
begin and end, and the types those methods return (i.e. iterators) have
dereference, inequality and pre-increment.
int x = 1;
for ( int v : q )
assert( v == x++ );
That went rather well, let’s just check that the order of removal is the
same as the order of insertion (first in, first out). This is how queues
should behave.
assert( q.pop() == 1 );
assert( q.pop() == 2 );
assert( q.pop() == 3 );
assert( q.empty() );
}
7.d.2 [finexp] We will do a simpler version of regular expressions that
can only capture finite languages, but somewhat more compactly than
just listing all the words that belong to the language. There will be two
operations: concatenation and alternative.
In this and the next demo, we will make use of late dispatch, which
will be properly explained in the next chapter. All you need to know
for now is, that, given:
• a class base and its derived class derived,
• a pointer, base *ptr, that in fact points to an instance of class derived,
and
• a method late which is marked virtual in base, and override in
derived,
a call ptr->late() will execute the implementation of the method from
derived (and not from base, as would be the case with a non-virtual
method).
Our goal will be to implement class finexp, with the following interface:
• an instance of finexp can be constructed from a string; the resulting
finexp will match that exact string and nothing else
• two instances of finexp can be combined using *: the resulting
finexp matches if the input string can be split in such a way that
the first part matches the left finexp and the second part matches
the right finexp
• two instances of finexp can be comined using +: the result matches
a string if either of the operands does
Hint: it might be a worthwhile exercise to compare the below implementation
with one based on std::shared_ptr.
struct node;
using node_ptr = std::unique_ptr< node >;
TBD explain things!
struct node
{
std::string x;
node_ptr l, r;
virtual std::set< int > match( const std::string &s ) const
{
assert( !l && !r );
if ( s.substr( 0, x.size() ) == x )
return { int( x.size() ) };
else
return {};
}
node_ptr copy_into( node_ptr &&n ) const
{
n->l = l ? l->clone() : nullptr;
n->r = r ? r->clone() : nullptr;
return std::move( n );
}
virtual node_ptr clone() const
{
return copy_into( std::make_unique< node >( x ) );
}
node( std::string x ) : x( x ) {}
node( const node_ptr &l_, const node_ptr &r_ )
: l( l_->clone() ), r( r_->clone() )
{}
virtual ~node() = default;
};
struct alt : node
{
using node::node;
node_ptr clone() const override
{
return copy_into( std::make_unique< alt >( x ) );
}
PB161 Programming in C++ 45/114 June 28, 2022
std::set< int > match( const std::string &s ) const override
{
std::set< int > lout = l->match( s ), rout = r->match( s );
rout.insert( lout.begin(), lout.end() );
return rout;
}
};
struct seq : node
{
using node::node;
node_ptr clone() const override
{
return copy_into( std::make_unique< seq >( x ) );
}
std::set< int > match( const std::string &s ) const override
{
std::set< int > out;
for ( int i : l->match( s ) )
for ( int j : r->match( s.substr( i ) ) )
out.insert( i + j );
return out;
}
};
class finexp
{
node_ptr n;
public:
finexp( std::string s ) : n( new node( s ) ) {}
finexp( node_ptr &&p ) : n( std::move( p ) ) {}
finexp( const finexp &o ) : n( o.n->clone() ) {}
finexp operator+( finexp b ) const
{
return { std::make_unique< alt >( n, b.n ) };
}
finexp operator*( finexp b ) const
{
return { std::make_unique< seq >( n, b.n ) };
}
friend bool match( const finexp &f, const std::string &s )
{
return f.n->match( s ).count( s.size() );
}
};
int main() /* demo */
{
finexp a( "a" ), b( "b" ), ab( "ab" ), ba( "ba" ),
abba( "abba" );
assert( match( a, "a" ) );
assert( match( b, "b" ) );
assert( !match( a, "b" ) );
assert( !match( b, "a" ) );
assert( match( abba, "abba" ) );
assert( !match( abba, "a" ) );
assert( !match( abba, "abb" ) );
assert( !match( a, "ab" ) );
assert( match( a + b, "a" ) );
assert( match( a + b, "b" ) );
assert( !match( a + b, "ab" ) );
assert( !match( a + b, "c" ) );
assert( match( a + abba, "a" ) );
assert( !match( a + abba, "b" ) );
assert( match( a + abba, "abba" ) );
assert( match( ( ab + a ) * a, "aba" ) );
assert( match( ( a + ab ) * a, "aba" ) );
assert( !match( ( ba + ab ) * a, "ba" ) );
assert( match( a * ( ba + ab ), "aba" ) );
assert( !match( a * ( b + a ), "aba" ) );
}
7.d.3 [expr] In this example program, we will look at using shared
pointers and operator overloading to get a nicer version of our expression
examples, this time with sub-structure sharing: that is, doing
something like a + a will not duplicate the sub-expression a.
Like in week 7, we will define an abstract base class to represent the
nodes of the expression tree.
struct expr_base
{
virtual int eval() const = 0;
virtual ~expr_base() = default;
};
Since we will use (shared) pointers to expr_base quite often, we can save
ourselves some typing by defining a convenient type alias: expr_ptr
sounds like a reasonable name.
using expr_ptr = std::shared_ptr< expr_base >;
We will have two implementations of expr_base: one for constant values
(nothing much to see here),
struct expr_const : expr_base
{
const int value;
expr_const( int v ) : value( v ) {}
int eval() const override { return value; }
};
and another for operator nodes. Those are more interesting, because
they need to hold references to the sub-expressions, which are represented
as shared pointers.
struct expr_op : expr_base
{
enum op_t { add, mul } op;
expr_ptr left, right;
expr_op( op_t op, expr_ptr l, expr_ptr r )
: op( op ), left( l ), right( r )
{}
int eval() const override
{
if ( op == add ) return left->eval() + right->eval();
if ( op == mul ) return left->eval() * right->eval();
assert( false );
}
};
In principle, we could directly overload operators on expr_ptr, but we
would like to maintain the illusion that expressions are values. For
that reason, we will implement a thin wrapper that provides a more
natural interface (and also takes care of operator overloading). Again,
the expr class essentially provides Java-like object semantics – which is
quite reasonable for immutable objects like our expression trees here.
struct expr
{
expr_ptr ptr;
expr( int v ) : ptr( std::make_shared< expr_const >( v ) ) {}
expr( expr_ptr e ) : ptr( e ) {}
PB161 Programming in C++ 46/114 June 28, 2022
int eval() const { return ptr->eval(); }
};
The overloaded operators simply construct a new node (of type expr_op
and wrap it up in an expr instance.
expr operator+( expr a, expr b )
{
return { std::make_shared< expr_op >( expr_op::add,
a.ptr, b.ptr ) };
}
expr operator*( expr a, expr b )
{
return { std::make_shared< expr_op >( expr_op::mul,
a.ptr, b.ptr ) };
}
int main() /* demo */
{
expr a( 3 ), b( 7 ), c( 2 );
expr ab = a + b;
expr bc = b * c;
expr abc = a + b * c;
assert( a.eval() == 3 );
assert( b.eval() == 7 );
assert( ab.eval() == 10 );
assert( bc.eval() == 14 );
assert( abc.eval() == 17 );
}
7.d.4 [family] For many tasks, shared pointers (reference counting)
are quite adequate (see also Python). However, they do have a weak
spot: reference cycles. If you manage to create a loop of shared pointers,
the pointers on this cycle (and anything outside the cycle they point to)
will never be freed. That is unfortunate, since it reintroduces memory
leaks into the rather leak-free subset of C++ that we have been using
until now.
However, if we are a little careful, C++ allows us to have cyclic data
structures with reference counting without introducing memory leaks:
the std::weak_ptr class template.
We will implement a bit of genealogy – that is, family trees. This will
simply consist of a graph of person instances (we will not delve into too
much detail). Each person will have two parents, a father and a mother,
and a list of children. We will want to maintain an invariant: the list of
children contains exactly those person instances that have this person
set as one of their parents. Since a fixed number of pointers (parents)
are easier to manage than the arbitrary number of children, we will
treat parents as the primary information and children as derived. Like
before, we will split the class into a shared (data) part and into thin
interface part.
class person_data
{
std::shared_ptr< person_data > mother, father;
std::vector< std::weak_ptr< person_data > > children;
std::string name;
friend class person;
};
The interface: the data is stored behind a shared pointer, but like in earlier
examples, we pretend the person instances are values with sharing
semantics. The family graph is, on the outside, still quite immutable (we
can only add and remove nodes), so the abstraction is still reasonably
solid.
class person
{
using data_ptr = std::shared_ptr< person_data >;
data_ptr _d;
public:
Construct a person instance from an existing data pointer. We would
actually like to make this private, but that would give us problems
because we actually delegate the constructor call to std::vector: we
would have to make that a friend class (but that would punch holes
into the model... let’s not bother for now).
explicit person( data_ptr p ) : _d( p ) {}
We need to be able to construct parent-less instances, since the data
ends somewhere and we can no longer provide the data about parents.
explicit person( std::string name )
: _d( std::make_shared< person_data >() )
{
_d->name = name;
}
The standard constructor for person, with two parents. We take person
by value since it’s really just a pointer anyway (we could perhaps save
an refcount increment/decrement pair by passing via const references).
We also use constructor delegation: in the initialization section, we
invoke the above ‘parent-less‘ constructor. This constructor is also
in charge of maintaining (half of) the above-mentioned invariant by
inserting our data pointer into the children list of both the parents.
person( std::string name, person mother, person father )
: person( name )
{
_d->mother = mother._d;
_d->father = father._d;
_d->mother->children.emplace_back( _d );
_d->father->children.emplace_back( _d );
}
The other half of the invariant is maintained here, with the help of
shared_ptr destructors: if a person is completely destroyed (i.e. no
copies remain, i.e. the reference count on the corresponding person_data
drops to zero), all weak_ptr instances pointing to it will automatically
turn into null pointers. We then simply filter those out to
obtain the correct list of children.
std::vector< person > children() const
{
std::vector< person > out;
for ( const auto &c_weak : _d->children )
if ( auto c = c_weak.lock() )
out.emplace_back( c );
return out;
}
A few simple accessors.
bool valid() const { return !!_d; }
std::string name() const { return _d->name; }
person mother() const { return person{ _d->mother }; }
person father() const { return person{ _d->father }; }
Equality: we base equality on object identity: copies of the same person
(even those that arise in a roundabout way, without calling the copy
constructor, e.g. those that arise from the above mother and father
accessors which construct new person instances) will compare as equal.
bool operator==( person o ) const { return o._d == _d; }
};
int main() /* demo */
{
person unknown( "unknown" );
person a( "a", unknown, unknown );
PB161 Programming in C++ 47/114 June 28, 2022
person b( "b", unknown, unknown );
assert( a.mother().valid() );
assert( a.father().valid() );
assert( a.mother() == unknown );
assert( a.father() == unknown );
assert( !unknown.mother().valid() );
assert( a.mother().name() == "unknown" );
{
person c( "c", a, b );
person d( "d", a, b );
person x( "x", unknown, unknown );
person e( "e", c, x );
Check that the children containers are correctly filled in by the con-
structors.
assert( c.mother() == a );
assert( a.children().size() == 2 );
assert( b.children().size() == 2 );
assert( c.children().size() == 1 );
assert( x.children().size() == 1 );
for ( const auto &ch : x.children() )
assert( ch == e );
for ( const auto &ch : c.children() )
assert( ch == e );
The instances c, d, x and e are destroyed at this point (with no surviving
copies).
}
Check that the invariant is maintained.
assert( a.children().empty() );
assert( b.children().empty() );
}
Part 7.e: Elementary Exercises
7.e.1 [dynarray] Implement a dynamic array of integers with 2 operations:
element access (using operator[]) and resize. The constructor
takes the initial size as its only parameter.
class dynarray;
7.e.2 [list] Implement a linked list of integers, with head, tail (returns
a reference) and empty. Asking for a head or tail of an empty list has
undefined results. A default-constructed list is empty. The other constructor
takes an int (the value of head) and a reference to an existing
list. It will should make a copy of the latter.
class list;
Part 7.p: Preparatory Exercises
7.p.1 [unrolled] Another exercise, another data structure. This time
we will look at so-called unrolled linked lists. We will need the data
structure itself, with begin, end, empty and push_back methods. As usual,
we will store integers. The difference between a ‘normal’ singly-linked
list and an unrolled list is that in the latter, each node stores more
than one item. In this case, we will use 4 items per node. Of course,
the last node might only be filled partially. The iterator that begin
and end return should at least implement dereference, pre-increment
and inequality, as usual. We will not provide an interface for erasing
elements, because that is somewhat tricky.
struct unrolled_node; /* ref: 6 lines */
struct unrolled_iterator; /* ref: 22 lines */
class unrolled; /* ref: 36 lines */
7.p.2 [bittrie] More data structures. A bit trie (or a bitwise trie, or a
bitwise radix tree) is a binary tree for encoding a set of binary values,
with quick insertion and lookup. Each edge in the tree encodes a
single bit (i.e. it carries a zero or a one). To make our life easier, we will
represent the keys using a vector of booleans.
The key is a sequence of bits: iteration order (left to right) corresponds
to a path through the trie starting from the root. I.e. the leftmost bit
decides whether to go left or right from the root, and so on. A key is
present in the trie iff it describes a path to a leaf node.
using key = std::vector< bool >;
struct trie_node; /* ref: 5 lines */
For simplicity, we will not have a normal insert method. Instead, the
trie will expose its root node via root and allow explicit creation of
new nodes via make, which accepts the parent node and a boolean
as arguments (the latter indicating whether the newly created edge
represents a 0 or a 1). Both root and make should return node references.
Finally, add a has method which will check whether a given key is
present in the trie.
class trie; /* ref: 21 lines */
7.p.3 [solid] In this exercise, we will focus on building objects that
have optional data attached to them. The idea is that if the optional
data is sufficiently big and there are enough instances which do not
use this data, it makes sense to split the object into two. Of course,
logically (in the interface), the object should still act like a single unit.
To make testing easier, we declare a global counter of matrices. It
will be adjusted by the constructor and destructor of transform_matrix
below. This is not a design pattern that you should normally use (but
it is okay in a small demo).
int matrix_counter = 0;
The two pieces will be, in this case, a general description of a 3D object
(a solid) and a 3D transformation matrix with 9 entries (3 rows and
3 columns). The matrix is represented by the class declared below.
Make the class default-constructible and do not forget to implement
the book-keeping for matrix_counter. The class should store the matrix
entries inline (i.e. they should be part of the object, not managed in a
separate heap allocation).
struct transform_matrix;
We don’t know about inheritance yet, but the below class could be
considered a base class in a simple inheritance hierarchy: it will only
have properties common to different object types, but will not describe
a complete solid in itself. It should have the following methods:
• pos_x, pos_y and pos_z to give the position of the solid
• transform_entry( int r, int c ) gives the entry in the transformation
matrix at row r and column c
• transform_set( int r, int c, double v ) sets the corresponding
entry in the transformation matrix
• a constructor which takes 3 arguments of type double (the x, y and
z position coordinates)
The default transformation matrix is the identity matrix (1’s on the
main diagonal, 0’s everywhere else). Memory should only be allocated
for the transformation matrix if it changes from the default.
class solid;
7.p.4 [chartrie] An exercise similar to the bittrie earlier (same data
PB161 Programming in C++ 48/114 June 28, 2022
structure but with bigger keys). To make it more interesting, the node
management will happen within the class itself and will not be part of
the interface. The encoding you should use is this:
• the left child of a node adds a single character to the key, like in the
bit trie from before (the character is part of the left edge)
• the right child is actually a sibling of the current node and the edge
is not labelled
• the chain to the right is sorted in ascending order
In other words, you can imagine the trie to be a 256-ary tree, which is
obviously impractical to implement directly (this would need 256 pointers
per node). Hence, we encode each ‘virtual’ node in this 256-ary
trie using a singly-linked list made of the right children of each real,
binary node.
struct trie_node; /* ref: 9 lines */
The interface of `trie` is very simple: it has an add method, which
inserts a key into the data structure, and a has method which decides
whether a given key is present. Both accept a single std::string. Like
with the bit trie before, we do not consider prefixes of included keys to
be present.
class trie; /* ref: 53 lines; has() = 10, add() = 36 */
7.p.5 [bdd] Binary decision diagrams are a compact way to write
boolean functions in multiple arguments. You could think of the data
structure as a DAG with additional semantics: each vertex is either a
variable and has two successors which tell us where to go next depending
on the value of that variable, or is a 0 or 1, represented by two sink
nodes in the DAG (there are no outgoing edges).
The interface should be as follows;
• the constructor takes a char: the variable to use for the root node
• one returns the true node
• zero returns the false node
• root returns the initial node
• add_var takes a char and creates a new variable node: there may be
multiple nodes for the same variable
• add_edge takes the parent node, a boolean, and the child
• eval takes a map from char to bool and returns true or false by
traversing the BDD from the root and at each variable node, taking
the path dictated by the input map (variable assignment)
Note: It is UB if a variable node does not have both successors set.
class bdd_node; /* ref: 6 lines */
class bdd; /* ref: 19 lines */
7.p.6 [rope] A rope is a string-like data structure, represented as a
binary tree with traditional strings in leaves and weights in internal
nodes. Subtree sharing is allowed and expected.
A weight of a given node is the total length of the string represented
by its left subtree. Provides an O(1) concatenation and O(d) indexing,
where d is the depth of the tree.
In addition to the indexing operator, provide 2 constructors: one which
constructs a singleton rope from a string, and another that joins 2
existing ropes.
You do not need to implement any rebalancing.
class rope;
Part 7.r: Regular Exercises
7.r.1 [circular] In this exercise, we will implement a slightly unusual
data structure: a circular linked list, but instead of the usual access
operators and iteration, it will have a rotate method, which rotates the
entire list. We require that rotation does not invalidate any references
to elements in the list.
If you think of the list as a stack, you can think of the rotate operation
as taking an element off the top and putting it at the bottom of the
stack. It is undefined on an empty list.
To add and remove elements, we will implement push and pop which
work in a stack-like manner. Only the top element is accessible, via
the top method. This method should allow both read and write access.
Finally, we also want to be able to check whether the list is empty. As
always, we will store integers in the data structure.
class circular;
7.r.2 [zipper] Implement our favourite data structure – a zipper of
integers – this time using a unique_ptr-linked list extending both ways
from the focus. Methods:
• (constructor) constructs a singleton zipper from an integer,
• shift_left and shift_right move the point of focus, in O(1), to the
nearest left (right) element; they return true if this was possible,
otherwise they return false and do nothing,
• push_left and push_right add a new element just left (just right) of
the current focus, again in O(1),
• focus access the current item (read and write).
7.r.3 [segment] In this exercise, we will go back to building data structures,
in this particular case a simple binary tree. The structure should
represent a partitioning of an interval with integer bounds into a set
of smaller, non-overlapping intervals.
Implement class segment_map with the following interface:
• the constructor takes two integers, which represent the limits of
the interval to be segmented,
• a split operation takes a single integer, which becomes the start of
a new segment, splitting the existing segment in two,
• query, given an integer n, returns the bounds of the segment that
contains n, as an std::pair of integers.
The tree does not need to be self-balancing: the order of splits will
determine the shape of the tree.
7.r.4 [diff] In this exercise, we will implement automatic differentiation
of simple expressions. You will need the following rules:
• linearity: (a ⋅ f(x) + b ⋅ g(x))′ = a ⋅ f′(x) + b ⋅ g′(x)
• the Leibniz rule: (f(x) ⋅ g(x))′ = f′(x) ⋅ g(x) + f(x) ⋅ g′(x)
• chain rule: (f(g(x)))′ = f′(g(x)) ⋅ g′(x)
• derivative of exponential: exp′(x) = exp(x)
Define a type, expr (from expression), such that values of this type can
be constructed from integers, added and multiplied, and exponentiated
using function expnat (to avoid conflicts with the exp in the standard
library).
class expr; /* ref: 29 + 7 lines */
expr expnat( expr );
Implement function diff that accepts a single expr and returns the
derivative (again in the form of expr). Define a constant x of type expr
such that diff( x ) is 1.
expr diff( expr ); /* ref: 11 lines */
// const expr x;
Finally, implement function eval which takes an expr and a double and
it substitutes for x and computes the value of the expression.
double eval( expr, double ); /* ref: 11 lines */
7.r.5 [critbit]
class cb_tree;
bool cb_dir( uint8_t key, uint8_t mask )
{
return ( 1 + ( mask | key ) ) >> 8;
PB161 Programming in C++ 49/114 June 28, 2022
}
bool cb_dir( std::string_view key, int byte, uint8_t mask )
{
return cb_dir( byte < key.size() ? key[ byte ] : 0, mask );
}
bool contains( const cb_tree &tree, std::string_view key )
{
auto n = tree.root(), last = tree.root();
bool last_internal = false;
if ( n )
while ( n->internal() )
{
bool dir = cb_dir( key, n->byte(), n->mask() );
n = dir ? n->right() : n->left();
}
return r;
}
Part 8: Inheritance and Polymorphism
This week will be about objects in the OOP (object-oriented programming)
sense and about inheritance-based polymorphism. In OOP,
classes are rarely designed in isolation: instead, new classes are derived
from an existing base class (the derived class inherits from the
base class). The derived class retains all the attributes (data) and methods
(behaviours) of the base (parent) class, and usually adds something
on top, or at least modifies some of the behaviours.
So far, we have worked with composition (though we rarely called
it that). We say objects (or classes) are composed when attributes of
classes are other classes (e.g. standard containers). The relationship
between the outer class and its attributes is known as ‘has-a’: a circle
has a center, a polynomial has a sequence of coefficients, etc.
Inheritance gives rise to a different type of relationship, known as ‘is-a’:
a few stereotypical examples:
• a circle is a shape,
• a ball is a solid, a cube is a solid too,
• a force is a vector (and so is velocity).
This is where polymorphism comes into play: a function which doesn’t
care about the particulars of a shape or a solid or a vector can accept
an instance of the base class. However, each instance of a derived class
is an instance of the base class too, and hence can be used in its place.
This is known as the Liskov substitution principle.
An important caveat: this does not work when passing objects by value,
because in general, the base class and the derived class do not have the
same size. Languages like Python or Java side-step this issue by always
passing objects by reference. In C++, we have to do that explicitly if
we want to use inheritance-based polymorphism. Of course, this also
works with pointers (including smart ones, like std::unique_ptr).
With this bit of theory out of the way, let’s look at some practical examples:
the rest of theory (late binding in particular) will be explained
in demonstrations:
1. account – a simple inheritance example
2. shapes – polymorphism and late dispatch
3. expr – dynamic and static types, more polymorphism
4. destroy – virtual destructors
5. factory – polymorphic return values
Elementary exercises:
1. resistance – compute resistance of a simple circuit
2. perimeter – shapes and their perimeter length
3. fight – rock, paper and scissors
Preparatory exercises:
1. prisoner – the famous dilemma
2. bexpr – boolean expressions with variables
3. sexpr – a tree made of lists (lisp style)
4. network – a network of counters
5. filter – filter items from a data source
6. geometry – shapes and visitors
Regular exercises:
1. bom – polymorphism and collections
2. circuit – calling virtual methods within the class
3. loops – circuits with loops
4. pretty – turn arithmetic expressions into strings
5. json – a more general JSON pretty-printer
6. while – interpreting while programs using an AST
Part 8.d: Demonstrations
8.d.1 [account] In this example, we will demonstrate the syntax and
most basic use of inheritance. Polymorphism will not enter the picture
yet (but we will get to that very soon: in the next example). We will
consider bank accounts (a favourite subject, surely).
We will start with a simple, vanilla account that has a balance, can
withdraw and deposit money. We have seen this before.
class account
{
The first new piece of syntax is the protected keyword. This is related
to inheritance: unlike private, it lets subclasses (or rather subclass
methods) access the members declared in a protected section. We also
notice that the balance is signed, even though in this class, that is not
strictly necessary: we will need that in one of the subclasses (yes, the
system is already breaking down a little).
protected:
int _balance;
public:
We allow an account to be constructed with an initial balance. We also
allow it to be default-constructed, initializing the balance to 0.
account( int initial = 0 )
: _balance( initial )
{}
Standard stuff.
bool withdraw( int sum )
{
if ( _balance > sum )
{
_balance -= sum;
return true;
}
return false;
}
void deposit( int sum ) { _balance += sum; }
int balance() const { return _balance; }
};
PB161 Programming in C++ 50/114 June 28, 2022
With the base class in place, we can define a derived class. The syntax
for inheritance adds a colon, :, after the class name and a list of classes
to inherit from, with access type qualifiers. We will always use public
inheritance. Also, did you know that naming things is hard?
class account_with_overdraft : public account
{
The derived class has, ostensibly, a single attribute. However, all the
attributes of all base classes are also present automatically. That is,
there already is an int _balance attribute in this class, inherited from
account. We will use it below.
protected:
int _overdraft;
public:
This is another new piece of syntax that we will need: a constructor of
a derived class must first call the constructors of all base classes. Since
this happens before any attributes of the derived class are constructed,
this call comes first in the initialization section. The derived-class
constructor is free to choose which (overloaded) constructor of the
base class to call. If the call is omitted, the default constructor of the
base class will be called.
account_with_overdraft( int initial = 0, int overdraft = 0 )
: account( initial ), _overdraft( overdraft )
{}
The methods defined in a base class are automatically available in the
derived class as well (same as attributes). However, unlike attributes,
we can replace inherited methods with versions more suitable for the
derived class. In this case, we need to adjust the behaviour of withdraw.
bool withdraw( int sum )
{
if ( _balance + _overdraft > sum )
{
_balance -= sum;
return true;
}
return false;
}
};
Here is another example based on the same language features.
class account_with_interest : public account
{
protected:
int _rate; /* percent per annum */
public:
account_with_interest( int initial = 0, int rate = 0 )
: account( initial ), _rate( rate )
{}
In this case, all the inherited methods can be used directly. However,
we need to add a new method, to compute and deposit the interest.
Since naming things is hard, we will call it next_year. The formula is
also pretty lame.
void next_year()
{
_balance += ( _balance * _rate ) / 100;
}
};
The way objects are used in this exercise is not super useful: the goal
was to demonstrate the syntax and basic properties of inheritance. In
modern practice, code re-use through inheritance is frowned upon
(except perhaps for mixins, which are however out of scope for this
subject). The main use-case for inheritance is subtype polymorphism,
which we will explore in the next unit, shapes.cpp.
int main() /* demo */
{
We first make a normal account and check that it behaves as expected.
Nothing much to see here.
account a( 100 );
assert( a.balance() == 100 );
assert( a.withdraw( 50 ) );
assert( !a.withdraw( 100 ) );
a.deposit( 10 );
assert( a.balance() == 60 );
Let’s try the first derived variant, an account with overdraft. We notice
that it’s possible to have a negative balance now.
account_with_overdraft awo( 100, 100 );
assert( awo.balance() == 100 );
assert( awo.withdraw( 50 ) );
assert( awo.withdraw( 100 ) );
awo.deposit( 10 );
assert( awo.balance() == -40 );
And finally, let’s try the other account variant, with interest.
account_with_interest awi( 100, 20 );
assert( awi.balance() == 100 );
assert( awi.withdraw( 50 ) );
assert( !awi.withdraw( 100 ) );
awi.deposit( 10 );
assert( awi.balance() == 60 );
awi.next_year();
assert( awi.balance() == 72 );
}
8.d.2 [shapes] The inheritance model in C++ is an instance of a more
general notion, known as subtyping. The defining characteristic of
subtyping is the Liskov substitution principle: a value which belongs
to a subtype (a derived class) can be used whenever a variable stores,
or a formal argument expects, a value that belongs to a supertype (the
base class). As mentioned earlier, in C++ this only extends to values
passed by reference or through pointers.
We will first define a couple useful type aliases to represent points and
bounding boxes.
using point = std::pair< double, double >;
using bounding_box = std::pair< point, point >;
Subtype polymorphism is, in C++, implemented via late binding: the
decision which method should be called is postponed to runtime (with
normal functions and methods, this happens during compile time).
The decision whether to use early binding (static dispatch) or late binding
(dynamic dispatch) is made by the programmer on a method-bymethod
basis. In other words, some methods of a class can use static
dispatch, while others use dynamic dispatch.
class shape
{
public:
To instruct the compiler to use dynamic dispatch for a given method,
put the keyword virtual in front of that method’s return type. Unlike
normal methods, a virtual method may be left unimplemented: this is
denoted by the = 0 at the end of the declaration. If a class has a method
like this, it is marked as abstract and it becomes impossible to create
instances of this class: the only way to use it is as a base class, through
PB161 Programming in C++ 51/114 June 28, 2022
inheritance. This is commonly done to define interfaces. In our case,
we will declare two such methods.
virtual double area() const = 0;
virtual bounding_box box() const = 0;
A class which introduces virtual methods also needs to have a destructor
marked as virtual. We will discuss this in more detail in a later
unit. For now, simply consider this to be an arbitrary rule.
virtual ~shape() = default;
};
As soon as the interface is defined, we can start working with arbitrary
classes which implement this interface, even those that have not been
defined yet. We will start by writing a simple polymorphic function
which accepts arbitrary shapes and computes the ratio of their area to
the area of their bounding box.
double box_coverage( const shape &s )
{
Hopefully, you remember structured bindings (if not, revisit e.g.
03/rel.cpp).
auto [ ll, ur ] = s.box();
auto [ left, bottom ] = ll;
auto [ right, top ] = ur;
return s.area() / ( ( right - left ) * ( top - bottom ) );
}
Another function: this time, it accepts two instances of shape. The
values it actually receives may be, however, of any type derived from
shape. In fact, a and b may be each an instances of a different derived
class.
bool box_collide( const shape &sh_a, const shape &sh_b )
{
A helper function (lambda) to decide whether a point is inside (or on
the boundary) of a bounding box.
auto in_box = []( const bounding_box &box, const point &pt )
{
auto [ x, y ] = pt;
auto [ ll, ur ] = box;
auto [ left, bottom ] = ll;
auto [ right, top ] = ur;
return x >= left && x <= right && y >= bottom && y <= top;
};
auto [ a, b ] = sh_a.box();
auto box = sh_b.box();
The two boxes collide if either of the corners of one is in the other box.
return in_box( box, a ) || in_box( box, b );
}
We now have the interface and two functions that are defined in terms
of that interface. To make some use of the functions, however, we need
to be able to make instances of shape, and as we have seen earlier, that
is only possible by deriving classes which provide implementations of
the virtual methods declared in the base class. Let’s start by defining a
circle.
class circle : public shape
{
point _center;
double _radius;
public:
The base class has a default constructor, so we do not need to explicitly
call it here.
circle( point c, double r ) : _center( c ), _radius( r ) {}
Now we need to implement the virtual methods defined in the base
class. In this case, we can omit the virtual keyword, but we should
specify that this method overrides one from a base class. This informs
the compiler of our intention to provide an implementation to an inherited
method and allows it (the compiler) to emit a warning in case we
accidentally hide the method instead, by mistyping the signature. The
most common mistake is forgetting the trailing const. Please always
specify override where it is applicable.
double area() const override
{
return 4 * std::atan( 1 ) * std::pow( _radius, 2 );
}
Now the other virtual method.
bounding_box box() const override
{
auto [ x, y ] = _center;
double r = _radius;
return { { x - r, y - r }, { x + r, y + r } };
}
};
And a second shape type, so we can actually make some use of polymorphism.
Everything is the same as above.
class rectangle : public shape
{
point _ll, _ur; /* lower left, upper right */
public:
rectangle( point ll, point ur ) : _ll( ll ), _ur( ur ) {}
double area() const override
{
auto [ left, bottom ] = _ll;
auto [ right, top ] = _ur;
return ( right - left ) * ( top - bottom );
}
bounding_box box() const override
{
return { _ll, _ur };
}
};
int main() /* demo */
{
We cannot directly construct a shape, since it is abstract, i.e. it has unimplemented
pure virtual methods. However, both circle and rectangle
provide implementations of those methods which we can use.
rectangle square( { 0, 0 }, { 1, 1 } );
assert( square.area() == 1 );
assert( square.box() == bounding_box( { 0, 0 }, { 1, 1 } ) );
assert( box_coverage( square ) == 1 );
circle circ( { 0, 0 }, 1 );
Check that the area of a unit circle is π, and the ratio of its area to its
bounding box is π / 4.
double pi = 4 * std::atan( 1 );
assert( std::fabs( circ.area() - pi ) < 1e-10 );
assert( std::fabs( box_coverage( circ ) - pi / 4 ) < 1e-10 );
PB161 Programming in C++ 52/114 June 28, 2022
The two shapes quite clearly collide, and if they collide, their bounding
boxes must also collide. A shape should always collide with itself, and
collisions are symmetric, so let’s check that too.
assert( box_collide( square, circ ) );
assert( box_collide( circ, square ) );
assert( box_collide( square, square ) );
assert( box_collide( circ, circ ) );
Let’s make a shape a bit further out and check the collision detection
with that.
circle c1( { 2, 3 }, 1 ), c2( { -1, -1 }, 1 );
assert( !box_collide( circ, c1 ) );
assert( !box_collide( c1, c2 ) );
assert( !box_collide( c1, square ) );
assert( box_collide( c2, square ) );
}
8.d.3 [expr] To better understand polymorphism, we will need to set
up some terminology, particularly:
• the notion of a static type, which is, essentially, the type written
down in the source code, and of a
• dynamic type (also known as a runtime type), which is the actual
type of the value that is stored behind a given reference (or pointer).
The relationship between the static and dynamic type may be:
• the static and dynamic type are the same (this was always the case
until this week), or
• the dynamic type may be a subtype of the static type (we will see
that in a short while).
Anything else is a bug.
We will use a very simple representation of arithmetic expressions as
our example here. An expression is a tree, where each node carries
either a value or an operation. We will want to explicitly track the
type of each node, and for that, we will use an enumerated type. Those
work the same as in C, but if we declare them using enum class, the
enumerated names will be scoped: we use them as type::sum, instead
of just sum as would be the case in C.
enum class type { sum, product, constant };
Now for the class hierarchy. The base class will be node.
class node
{
public:
The first thing we will implement is a static_type method, which tells
us the static type of this class. The base class, however, does not have
any sensible value to return here, so we will just throw an exception.
type static_type() const
{
throw std::logic_error( "bad static_type() call" );
}
The ‘real’ (dynamic) type must be a virtual method, since the actual
implementation must be selected based on the dynamic type: this is
exactly what late binding does. Since the method is virtual, we do not
need to supply an implementation if we can’t give a sensible one.
virtual type dynamic_type() const = 0;
The interesting thing that is associated with each node is its value.
For operation nodes, it can be computed, while for leaf nodes (type
constant), it is simply stored in the node.
virtual int value() const = 0;
We also observe the virtual destructor rule.
virtual ~node() = default;
};
We first define the (simpler) leaf nodes, i.e. constants.
class constant : public node
{
int _value;
public:
The leaf node constructor simply takes an integer value and stores it
in an attribute.
constant( int v ) : _value( v ) {}
Now the interface common to all node instances:
type static_type() const { return type::constant; }
In methods of class constant, the static type of this is always7
either constant
* or const constant *. Hence we can simply call the static_type
method, since it uses static dispatch (it was not declared virtual in the
base class) and hence the call will always resolve to the method just
above.
type dynamic_type() const override { return static_type(); }
Finally, the ‘business’ method:
int value() const override { return _value; }
};
The inner nodes of the tree are operations. We will create an intermediate
(but still abstract) class, to serve as a base for the two operation
classes which we will define later.
class operation : public node
{
const node &_left, &_right;
public:
operation( const node &l, const node &r )
: _left( l ), _right( r )
{}
We will leave static_type untouched: the version from the base class
works okay for us, since there is nothing better that we could do here.
The dynamic_type and value stay unimplemented.
We are facing a dilemma here, though. We would like to add accessors
for the children, but it is not clear whether to make them virtual or not.
Considering that we keep the references in attributes of this class, it
seems unlikely that the implementation of the accessors would change
in a subclass and we can use cheaper static dispatch.
const node &left() const { return _left; }
const node &right() const { return _right; }
};
Now for the two operation classes.
class sum : public operation
{
public:
The base class does not have a default constructor, which means we
need to call the one that’s available manually.
7
As long as we pretend that the volatile keyword does not exist, which is an entirely reasonable
thing to do.
PB161 Programming in C++ 53/114 June 28, 2022
sum( const node &l, const node &r )
: operation( l, r )
{}
We want to replace the static_type implementation that was inherited
from node (through operation):
type static_type() const { return type::sum; }
And now the (dynamic-dispatch) interface mandated by the (indirect)
base class node. We can use the same approach that we used in constant
for dynamic_type:
type dynamic_type() const override { return static_type(); }
And finally the logic. The static return type of left and right is const
node &, but the method we call on each, value, uses dynamic dispatch
(it is marked virtual in class node). Therefore, the actual method which
will be called depends on the dynamic type of the respective child node.
int value() const override
{
return left().value() + right().value();
}
};
Basically a re-run of sum.
class product : public operation
{
public:
We will use a trick which will allow us to not type out the (boring and
redundant) constructor. If all we want to do is just forward arguments
to the parent class, we can use the following syntax. You do not have
to remember it, but it can save some typing if you do.
using operation::operation;
Now the interface methods.
type static_type() const { return type::product; }
type dynamic_type() const override { return static_type(); }
int value() const override
{
return left().value() * right().value();
}
};
int main() /* demo */
{
Instances of class constant are quite straightforward. Let’s declare
some.
constant const_1( 1 ),
const_2( 2 ),
const_m1( -1 ),
const_10( 10 );
The constructor of sum accepts two instances of node, passed by reference.
Since constant is a subclass of node, it is okay to use those, too.
sum sum_0( const_1, const_m1 ),
sum_3( const_1, const_2 );
The product constructor is the same. But now we will also try using
instances of sum, since sum is also derived (even if indirectly) from node
and therefore sum is a subtype of node, too.
product prod_4( const_2, const_2 ),
prod_6( const_2, sum_3 ),
prod_40( prod_4, const_10 );
Let’s also make a sum instance which has children of different types.
sum sum_9( sum_3, prod_6 );
For all variables which hold values (i.e. not references), static type =
dynamic type. To make the following code easier to follow, the static
type of each of the above variables is explicitly mentioned in its name.
Clearly, we can call the value method on the variables directly and it
will call the right method.
assert( const_1.value() == 1 );
assert( const_2.value() == 2 );
assert( sum_0.value() == 0 );
assert( sum_3.value() == 3 );
assert( prod_4.value() == 4 );
assert( prod_6.value() == 6 );
assert( prod_40.value() == 40 );
assert( sum_9.value() == 9 );
However, the above results should already convince us that dynamic
dispatch works as expected: the results depend on the ability of
sum::value and product::value to call correct versions of the value
method on their children, even though the static types of the references
stored in operation are const node. We can however explore the
behaviour in a bit more detail.
const node &sum_0_ref = sum_0, &prod_6_ref = prod_6;
Now the static type of sum_0_ref is const node &, but the dynamic type
of the value to which it refers is sum, and for prod_6_ref the static type
is const node & and dynamic is product.
assert( sum_0_ref.value() == 0 );
assert( prod_6_ref.value() == 6 );
Let us also check the behaviour of left and right.
assert( sum_0.left().value() == 1 );
assert( sum_0.right().value() == -1 );
The static type through which we call left and right does not matter,
because neither product nor sum provide a different implementation of
the method.
const operation &op = sum_0;
assert( op.left().value() == 1 );
assert( op.right().value() == -1 );
The final thing to check is the static_type and dynamic_type methods.
By now, we should have a decent understanding of what to expect.
Please note that sum_0 and sum_0_ref refer to the same instance and
hence they have the same dynamic type, even though their static types
differ.
assert( sum_0.dynamic_type() == type::sum );
assert( sum_0_ref.dynamic_type() == type::sum );
assert( sum_0.static_type() == type::sum );
try { sum_0_ref.static_type(); assert( false ); }
catch ( const std::logic_error & ) {}
And the same is true about prod_6 and prod_6_ref.
assert( prod_6.dynamic_type() == type::product );
assert( prod_6_ref.dynamic_type() == type::product );
assert( prod_6.static_type() == type::product );
try { prod_6_ref.static_type(); assert( false ); }
catch ( const std::logic_error & ) {}
}
8.d.4 [destroy] In this (entirely synthetic, sorry) example, we will look
PB161 Programming in C++ 54/114 June 28, 2022
at object destruction, especially in the context of polymorphism.
We first set up a few counters to track constructor and destructor calls.
static int bad_base_counter = 0, bad_derived_counter = 0,
good_base_counter = 0, good_derived_counter = 0;
class bad_base
{
public:
virtual int bad_dummy() { return 0; }
bad_base() { bad_base_counter ++; }
We will knowingly break the virtual destructor rule here, to see why
the rule exists.
~bad_base() { bad_base_counter --; }
};
class good_base
{
public:
virtual int good_dummy() { return 0; }
good_base() { good_base_counter ++; }
Notice the virtual.
virtual ~good_base() { good_base_counter --; }
};
Let’s add some innocent derived classes.
class bad_derived : public bad_base
{
public:
bad_derived() { bad_derived_counter ++; }
~bad_derived() { bad_derived_counter --; }
};
class good_derived : public good_base
{
public:
good_derived() { good_derived_counter ++; }
It is good practice to also add override to destructors of derived classes.
This will tell the compiler we expect the base class to have a virtual
destructor which we are extending. The compiler will emit an error if
the base class destructor is (through some unfortunate accident) not
marked as virtual.
~good_derived() override { good_derived_counter --; }
};
int main() /* demo */
{
For regular variables, everything works as expected: constructors and
destructors of all classes in the hierarchy are called.
{
bad_base bb;
assert( bad_base_counter == 1 );
bad_derived bd;
assert( bad_base_counter == 2 );
assert( bad_derived_counter == 1 );
}
assert( bad_base_counter == 0 );
assert( bad_derived_counter == 0 );
Same thing with virtual destructors.
{
good_base gb;
assert( good_base_counter == 1 );
good_derived gd;
assert( good_base_counter == 2 );
assert( good_derived_counter == 1 );
}
assert( good_base_counter == 0 );
assert( good_derived_counter == 0 );
However, problems start if an instance is destroyed through a pointer
whose static type disagrees with the dynamic type. This cannot happen
with references (unless the destructor is called explicitly), but it is
entirely plausible with pointers, including smart pointers. Let’s first
demonstrate the case that works: good_derived.
using good_ptr = std::unique_ptr< good_base >;
Please make good note of the fact, that the static type of the pointer
refers to good_base, but the actual value stored in it has dynamic type
good_derived.
{
good_ptr gp = std::make_unique< good_derived >();
assert( good_base_counter == 1 );
assert( good_derived_counter == 1 );
}
Since the unique_ptr went out of scope, the instance stored behind it
was destroyed. The counters should be both zero again.
assert( good_base_counter == 0 );
assert( good_derived_counter == 0 );
Let’s observe what happens with the bad_base and bad_derived combi-
nation.
using bad_ptr = std::unique_ptr< bad_base >;
{
bad_ptr bp = std::make_unique< bad_derived >();
assert( bad_base_counter == 1 );
assert( bad_derived_counter == 1 );
}
The pointer went out of scope. Since the destructor was called using
static dispatch, only the base class destructor was called. This is of
course very problematic, since resources were leaked and invariants
broken.
assert( bad_base_counter == 0 );
assert( bad_derived_counter == 1 );
Please note that some compilers (recent clang versions) will emit a
warning if this happens. Unfortunately, this is not the case with gcc
9.2 which we are using (and which is a rather recent compiler). It
is therefore unadvisable to rely on the compiler to catch this type of
problem. Stay vigilant.
}
8.d.5 [factory] As we have seen, subtype polymorphism allows us to
define an interface in terms of virtual methods (that is, based on late
dispatch) and then create various implementations of this interface.
It is sometimes useful to create instances of multiple different derived
classes based on runtime inputs, but once they are created, to treat
them uniformly. The uniform treatment is made possible by subtype
polymorphism: if the entire interaction with these objects is done
through the shared interface, the instances are all, at the type level,
interchangeable with each other. The behaviour of those instances
will of course differ, depending on their dynamic type.
When a system is designed this way, the entire program uses a single
static type to work with all instances from the given inheritance
PB161 Programming in C++ 55/114 June 28, 2022
hierarchy – the type of the base class. Let’s define such a base class.
class part
{
public:
virtual std::string description() const = 0;
virtual ~part() = default;
};
Let’s add a simple function which operates on generic parts. Working
with instances is easy, since they can be passed through a reference
to the base type. For instance the following function which formats a
single line for a bill of materials (bom).
std::string bom_line( const part &p, int count )
{
return std::to_string( count ) + "x " + p.description();
}
However, creation of these instances poses a somewhat unique challenge
in C++: memory management. In languages like Java or C#, we
can create the instance and return a reference to the caller, and the
garbage collector will ensure that the instance is correctly destroyed
when it is no longer used. We do not have this luxury in C++.
Of course, we could always do memory management by hand, like
it’s 1990. Fortunately, modern C++ provides smart pointers in the
standard library, making memory management much easier and safer.
Recall that a unique_ptr is an owning pointer: it holds onto an object
instance while it is in scope and destroys it afterwards. Unlike objects
stored in local variables, though, the ownership of the instance held
in a unique_ptr can be transferred out of the function (i.e. an instance
of unique_ptr can be legally returned, unlike a reference to a local vari-
able).
This will make it possible to define a factory: a function which constructs
instances (parts) and returns them to the caller. Of course, to
actually define the function, we will need to define the derived classes
which it is supposed to create.
using part_ptr = std::unique_ptr< part >;
part_ptr factory( std::string );
In the program design outlined earlier, the derived classes change some
of the behaviours, or perhaps add data members (attributes) to the base
class, but apart from construction, they are entirely operated through
the interface defined by the base class.
class cog : public part
{
int teeth;
public:
cog( int teeth ) : teeth( teeth ) {}
std::string description() const override
{
return std::string( "cog with " ) +
std::to_string( teeth ) + " teeth";
}
};
class axle : public part
{
public:
std::string description() const override
{
return "axle";
}
};
class screw : public part
{
int _thread, _length;
public:
screw( int t, int l ) : _thread( t ), _length( l ) {}
std::string description() const override
{
return std::to_string( _length ) + "mm M" +
std::to_string( _thread ) + " screw";
}
};
Now that we have defined the derived classes, we can finally define
the factory function.
part_ptr factory( std::string desc )
{
We will use std::istringstream (first described in 06/streams.cpp) to
extract a description of the instance that we want to create from a
string. The format will be simple: the type of the part, followed by its
parameters separated by spaces.
std::istringstream s( desc );
std::string type;
s >> type; /* extract the first word */
if ( type == "cog" )
{
int teeth;
s >> teeth;
return std::make_unique< cog >( teeth );
}
if ( type == "axle" )
return std::make_unique< axle >();
if ( type == "screw" )
{
int thread, length;
s >> thread >> length;
return std::make_unique< screw >( thread, length );
}
throw std::runtime_error( "unexpected part description" );
}
int main() /* demo */
{
Let’s first use the factory to make some instances. They will be held
by part_ptr (i.e. unique_ptr with the static type part.
part_ptr ax = factory( "axle" ),
m7 = factory( "screw 7 50" ),
m3 = factory( "screw 3 10" ),
c8 = factory( "cog 8" ),
c9 = factory( "cog 9" );
From the point of view of the static type system, all the parts created
above are now the same. We can call the methods which were defined
in the interface, or we can pass them into functions which work with
parts.
assert( ax->description() == "axle" );
assert( m7->description() == "50mm M7 screw" );
assert( m3->description() == "10mm M3 screw" );
assert( c8->description() == "cog with 8 teeth" );
assert( c9->description() == "cog with 9 teeth" );
Let’s try using the bom_line function which we have defined earlier.
assert( bom_line( *ax, 3 ) == "3x axle" );
assert( bom_line( *m7, 20 ) == "20x 50mm M7 screw" );
At the end of the scope, the objects are destroyed and all memory is
PB161 Programming in C++ 56/114 June 28, 2022
automatically freed.
}
Part 8.e: Elementary Exercises
8.e.1 [resistance] We are given a simple electrical circuit made of resistors
and wires, and we want to compute the total resistance between
two points. The circuit is simple in the sense that in any given section,
all its immediate sub-sections are either connected in series or in
parallel. Here is an example:
R₂
R₁ R₅
R₃ R₄
A B
The resistance that we are interested in is between the points A and B.
Given R1 and R2 connected in series, the total resistance is R = R1 +R2.
For the same resistors connected in parallel, the resistance is given by
1/R = 1/R1 + 1/R2.
You will implement 2 classes: series and parallel, each of which represents
a single segment of the circuit. Both classes shall provide a
method add, that will accept either a number (double) which will add
a single resistor to that segment, or a const reference to the opposite
class (i.e. an instance of series should accept a reference to parallel
and vice versa).
class series;
class parallel;
Then add a top-level function resistance, which accepts either a series
or a parallel instance and computes the total resistance of the circuit
described by that instance. The exact prototype is up to you.
8.e.2 [perimeter] Implement a simple inheritance hierarchy – the base
class will be shape, with a pure virtual method perimeter, the 2 derived
classes will be circle and rectangle. The circle is constructed from
a radius, while the rectangle from a width and height, all of them
floating-point numbers.
class shape;
class circle;
class rectangle;
bool check_shape( const shape &s, double p )
{
return std::fabs( s.perimeter() - p ) < 1e-8;
}
8.e.3 [fight] There should be 4 classes: the base class gesture and 3
derived: rock, paper and scissors. Class gesture has a (pure virtual)
method fight which takes another gesture (via a const reference) and
returns true if the current gesture wins.
To do this, add another method, visit, which has 3 overloads, one
each for rock, paper and scissors. Then override fight in each derived
class, to simply call visit( *this ) on the opposing gesture. The visit
method knows the type of both this and the opponent (via the overload)
– simply indicate the winner by returning an appropriate con-
stant.
class rock;
class paper;
class scissors;
Keep the forward declarations, you will need them to define the overloads
for visit.
class gesture;
Now define the 3 derived classes.
Part 8.p: Preparatory Exercises
8.p.1 [prisoner] Another exercise, another class hierarchy. The abstract
base class will be called prisoner, and the implementations will
be different strategies in the well-known game of (iterated) prisoner’s
dilemma.
The prisoner class should provide method betray which takes a boolean
(the decision of the other player in the last round) and returns the
decision of the player for this round. In general, the betray method
should not be const, because strategies may want to remember past
decisions (though we will not implement a strategy like that in this
exercise).
class prisoner;
Implement an always-betray strategy in class traitor, the tit-for-tat
strategy in vengeful and an always-cooperate in benign.
class traitor;
class vengeful;
class benign;
Implement a simple strategy evaluator in function play. It takes two
prisoners and the number of rounds and returns a negative number if
the first one wins, 0 if the game is a tie and a positive number if the
second wins. The scoring matrix:
• neither player betrays 2 / 2
• a betrays, b does not: 3 / 0
• a does not betray, b does: 0 / 3
• both betray 1 / 1
int play( prisoner &a, prisoner &b, int rounds );
8.p.2 [bexpr] Boolean expressions with variables, represented as binary
trees. Internal nodes carry a logical operation on the values
obtained from children while leaf nodes carry variable references.
To evaluate an expression, we will need to supply values for each of
the variables that appears in the expression. We will identify variables
using integers, and the assignment of values will be done through
the type input defined below. It is undefined behaviour if a variable
appears in an expression but is not present in the provided input value.
using input = std::map< int, bool >;
Like earlier in expr.cpp, the base class will be called node, but this time
will only define a single method: eval, which accepts a single input
argument (as a const reference).
class node; /* ref: 6 lines */
Internal nodes are all of the same type, and their constructor takes an
unsigned integer, table, and two node references. Assuming bit zero is
the lowest-order bit, the node operates as follows:
• false false → bit 0 of table
• false true → bit 1 of table
• true false → bit 2 of table
• true true → bit 3 of table
class operation; /* ref: 16 lines */
The leaf nodes carry a single integer (passed in through the constructor)
– the identifier of the variable they represent.
class variable; /* ref: 7 lines */
PB161 Programming in C++ 57/114 June 28, 2022
8.p.3 [sexpr] An s-expression is a tree in which each node has an
arbitrary number of children. To make things a little more interesting,
our s-expression nodes will own their children.
The base class will be called node (again) and it will have single (virtual)
method: value, with no arguments and an int return value.
class node;
using node_ptr = std::unique_ptr< node >;
There will be two types of internal nodes: sum and product, and in this
case, they will compute the sum or the product of all their children,
regardless of their number. A sum with no children should evaluate
to 0 and a product with no children should evaluate to 1.
Both will have an additional method: add_child, which accepts (by
value) a single node_ptr and both should have default constructors. It
is okay to add an intermediate class to the hierarchy.
class sum;
class product;
Leaf nodes carry an integer constant, given to them via a constructor.
class constant;
8.p.4 [network] In this exercise, we will define a network of counters,
where each node has its own counter which starts at zero, and events
which affect the counters propagate in the network. Different node
types react differently to the events.
There are three basic events which can propagate through the network:
reset will set the counter to 0, increment and decrement add and subtract
1, respectively.
enum class event { reset, increment, decrement };
The abstract base class, node, will define the polymorphic interface.
Methods:
• react with a single argument of type event,
• connect which will take a reference to another node instance: the
connection thus created starts in this and extends to the node given
in the argument,
• read, a const method that returns the current value of the counter.
Think carefully about which methods need to be virtual and which
don’t. The counter is signed and starts at 0. Each node can have an
arbitrary number of both outgoing and incoming connections.
class node;
Now for the node types. Each node type first applies the event to its
own counter, then propagates (or not) some event along all outgoing
connections. Implement the following node types:
• forward sends the same event it has received
• invert sends the opposite event
• gate resends the event if the new counter value is positive
class forward;
class invert;
class gate;
8.p.5 [filter] This exercise will be yet another take on a set of numbers.
This time, we will add a capability to filter the numbers on output.
It will be possible to change the filter applied to a given set at runtime.
The base class for representing filters will contain a single pure virtual
method, accept. The method should be marked const.
class filter;
The set (which we will implement below) will own the filter instance
and hence will use a unique_ptr to hold it.
using filter_ptr = std::unique_ptr< filter >;
The set should have standard methods: add and has, the latter of which
will respect the configured filter (i.e. items rejected by the filter will always
test negative on has). The method set_filter should set the filter.
If no filter is set, all numbers should be accepted. Calling set_filter
with a nullptr argument should clear the filter.
Additionally, set should have begin and end methods (both const) which
return very simple iterators that only provide dereference to an int
(value), pre-increment and inequality. It is a good idea to keep two
instances of std::set< int >::iterator in attributes (in addition to
a pointer to the output filter): you will need to know, in the preincrement
operator, that you ran out of items when skipping numbers
which the filter rejected.
class set_iterator;
class set;
Finally, implement a filter that only accepts odd numbers.
class odd;
8.p.6 [geometry] We will go back to a bit of geometry, this time with
circles and lines: in this exercise, we will be interested in planar intersections.
We will consider two objects to intersect when they have at
least one common point. On the C++ side, we will use a bit of a trick
with virtual method overloading (in a slightly more general setting,
the trick is known as the visitor pattern).
First some definitions: the familiar point.
using point = std::pair< double, double >;
Check whether two floating-point numbers are ‘essentially the same’
(i.e. fuzzy equality).
bool close( double a, double b )
{
return std::fabs( a - b ) < 1e-10;
}
We will need to use forward declarations in this exercise, since methods
of the base class will refer to the derived types.
struct circle;
struct line;
These two helper functions are already defined in this file and may
come in useful (like the slope class above).
double dist( point, point );
double dist( const line &, point );
A helper class which is constructed from two points. Two instances of
slope compare equal if the slopes of the two lines passing through the
respective point pairs are the same.
struct slope : std::pair< double, double >
{
slope( point p, point q )
: point( ( q.first - p.first ) / dist( p, q ),
( q.second - p.second ) / dist( p, q ) )
{}
bool operator==( const slope &o ) const
{
auto [ px, py ] = *this;
auto [ qx, qy ] = o;
return ( close( px, qx ) && close( py, qy ) ) ||
( close( px, -qx ) && close( py, -qy ) );
}
PB161 Programming in C++ 58/114 June 28, 2022
bool operator!=( const slope &o ) const
{
return !( *this == o );
}
};
Now we can define the class object, which will have a virtual method
intersects with 3 overloads: one that accepts a const reference to a
circle, another that accepts a const reference to a line and finally one
that accepts any object.
class object;
Put definitions of the classes circle and line here. A circle is given by
a point and a radius (double), while a line is given by two points. NB.
Make the line attributes public and name them p and q to make the
dist helper function work.
struct circle; /* ref: 18 lines */
struct line; /* ref: 18 lines */
Definitions of the helper functions.
double dist( point p, point q )
{
auto [ px, py ] = p;
auto [ qx, qy ] = q;
return std::sqrt( std::pow( px - qx, 2 ) +
std::pow( py - qy, 2 ) );
}
double dist( const line &l, point p )
{
auto [ x2, y2 ] = l.q;
auto [ x1, y1 ] = l.p;
auto [ x0, y0 ] = p;
return std::fabs( ( y2 - y1 ) * x0 - ( x2 - x1 ) * y0 +
x2 * y1 - y2 * x1 ) /
dist( l.p, l.q );
}
Part 8.r: Regular Exercises
8.r.1 [bom] Let’s revisit the idea of a bill of materials that made a brief
appearance in factory.cpp, but in a slightly more useful incarnation.
Define the following class hierarchy: the base class, part, should have
a (pure) virtual method description that returns an std::string. It
should also keep an attribute of type std::string and provide a getter
for this attribute called part_no() (part number). Then add 2 derived
classes:
• resistor which takes the part number and an integral resistance
as its constructor argument and provides a description of the form
"resistor ?Ω" where ? is the provided resistance,
• capacitor which also takes a part number and an integral capacitance
and provides a description of the form "capacitor ?μF" where
? is again the provided value.
class part;
class resistor;
class capacitor;
We will also use owning pointers, so let us define a convenient type
alias for that:
using part_ptr = std::unique_ptr< part >;
That was the mechanical part. Now we will need to think a bit: we
want a class bom which will remember a list of parts, along with their
quantities and will own the part instances it holds. The interface:
• a method add, which accepts a part_ptr by value (it will take ownership
of the instance) and the quantity (integer)
• a method find which accepts an std::string and returns a const
reference to the part instance with the given part number,
• a method qty which returns the associated quantity, given a part
number.
class bom;
8.r.2 [circuit] In this exercise, we will look at calling virtual methods
from within the class, in an ‘inverted’ approach to inheritance. Most
of the implementation will be part of the base class, in terms of a few
(or in this case one) protected virtual methods.
We will implement a simple class hierarchy to represent a logical circuit:
a bunch of components connected with wires. Each component
will have at most 2 inputs and a single output (all of which are boolean
values). Implement the following (non-virtual) methods:
• connect which takes an integer (0 or 1, the index of the input to
connect) and a reference to another component and connects the
output of the given component to the input of this component
• read with no arguments, which returns the current output of the
component (this will of course depend on the state of the input
components).
Both inputs start out unconnected. Unconnected inputs always read
out false. Behaviour is undefined if there is a loop in the circuit (but
see also loops.cpp).
class component;
The derived classes should be as follows:
• nand for which the output is the NAND logical function of the two
inputs,
• source which ignores both inputs and reads out true,
• delay which behaves as follows: first time read is called, it always
returns zero; subsequent read calls return a value that the input 0
had at the time of the previous call to read.
class nand;
class source;
class delay;
8.r.3 [loops] Same basic idea as circuit.cpp: we model a circuit made
of components. Things get a bit more complicated in this version:
• loops are allowed
• parts have 2 inputs and 2 outputs each
The base class, with the following interface:
• read takes an integer (decides which output) and returns a boolean,
• connect takes two integers and a reference to a component (the first
integer defines the input of this and the second integer defines the
output of the third argument to connect).
There is more than one way to resolve loops, some of which require
read to be virtual (that’s okay). Please note that each loop must have at
least one delay in it (otherwise, behaviour is still undefined). NB. Each
component should first read input 0 and then input 1: the ordering
will affect the result.
class component; /* ref: 30 lines */
A delay is a component that reads out, on both outputs, the value it
has obtained on the corresponding input on the previous call to read.
class delay; /* ref: 20 lines */
PB161 Programming in C++ 59/114 June 28, 2022
A latch remembers one bit of information (starting at false):
• if both inputs read false, the remembered bit remains unchanged,
• if input 0 is false while input 1 is true the remembered bit is set to
true,
• in all other cases, the remembered bit is set to false.
The value on output 0 is the new value of the remembered bit: there
is no delay. The value on output 1 is the negation of output 0.
class latch; /* 15 lines */
Finally, the cnot gate, or a controlled not gate has the following behav-
iour:
• output 0 always matches input 0, while
• output 1 is set to:
∘ input 1 if input 0 is true
∘ negation of input 1 if input 0 is false
class cnot; /* ref: 11 lines */
8.r.4 [pretty] In this exercise, we will write a pretty-printer for simple
arithmetic expressions, with 3 operation types: addition, multiplication
and equality, written as +, * and = respectively. The goal is to print the
expression with as few parentheses as possible.
Assume full associativity for all operations. The precedence order is
the usual one: multiplication binds most tightly, while equality most
loosely.
The formatting is done by calling a print method on the root of the
expression to be printed.
class node;
class addition;
class multiplication;
class equality;
class constant;
using node_ptr = std::unique_ptr< node >;
node_ptr read( std::string_view expr );
8.r.5 [json] The goal of this exercise is to implement a printer for JSON,
invoked as a print method available on each node. It should take no
arguments and return an instance of std::string. For simplicity, the
only scalar values you need to implement are integers. Then there are
2 composite data types:
• arrays, which represent a sequence of arbitrary values,
• objects, which map strings to arbitrary values.
Both composite types are heterogeneous (the items can be of different
types). They are formatted as follows:
• array: [ 1, [ 2, 3 ], 4 ],
• object: { "key₁": 7, "key₂": [ 1, 2 ] }.
To further simplify matters, we will not deal with line breaks or indentation
– format everything as a single line.
class node;
using node_ptr = std::unique_ptr< node >;
using node_ref = const node &;
The number class is to be constructed from an int, has no children, and
needs no methods besides print.
class number;
The object and array classes represent composite JSON data. They
should be both default-constructible, resulting in an empty collection.
Both should have an append method: for object, it takes an std::string
(the key) and a node_ptr, while for array, only the latter. In both cases,
print items in the order in which they were appended. Duplicated keys
are ignored (i.e. first occurrence wins).
class object;
class array;
8.r.6 [while] Consider an abstract syntax tree of a very simple imperative
programming language with structured control flow. Let there be
3 types of statements:
1. a variable increment, a ++,
2. a while loop of the form while (a != b) stmt, and finally
3. a block, which is a sequence of statements.
class statement;
using stmt_ptr = std::unique_ptr< statement >;
We will represent variables as strings. Provide an eval method which
takes variable assignment as an argument and returns the same as a
result. Variables used in the program but not given in the input start as
0. The variable assignment (i.e. the state of the program) is represented
as an std::map from strings to integers.
using state = std::map< std::string, int >;
The constructors should be as follows:
• stmt_inc takes the name of the variable to be incremented,
• stmt_while takes 2 variable names and an stmt_ptr for the body, and
• stmt_block is default-constructed as a noop, but provides an append
method to insert a stmt_ptr at the end.
class stmt_inc;
class stmt_while;
class stmt_block;
Part T.2: Tasks with Operators, Exceptions and OOP
The programming tasks for this block are as follows:
1. machine.* – a simple register machine simulator,
2. natural.* – arbitrary-size natural numbers,
3. parser.* – parsing simplified JSON,
4. complex.* – arbitrary-precision complex numbers.
The first task only relies on knowledge from the first block and you
should be able to start working on it immediately. Tasks 2 and 4 additionally
require operator overloading (chapter 5) and basic understanding
of exceptions (chapter 6). Finally, task 3 needs unique_ptr (chapter
7) and virtual dispatch (chapter 8), but the parser itself (and hence
xml_validate) can be implemented with knowledge from block 1 alone,
so you can still start early.
Part T.2.1: [complex]
In this exercise, you will implement exact (arbitrary-precision) real and
complex numbers. You can use the natural task as a base, if you wish.
Both real and complex numbers should provide the standard array of
arithmetic operators: addition, subtraction, unary minus, multiplication
and division. Real numbers should have all relational operators
and complex numbers should have equality (== and !=).
Note: keep your representation normalised – complexity of operations
PB161 Programming in C++ 60/114 June 28, 2022
should only depend on the represented number, not on the way it was
obtained.
// extra files: natural.hpp natural.cpp
class real
{
public:
explicit real( int v = 0 );
real abs() const;
real reciprocal() const;
real power( int n ) const;
};
class complex
{
static inline const real epsilon = real( 1 ) / real( 1000000 );
public:
explicit complex( real real_part = real( 0 ),
real imaginary_part = real( 0 ) );
real real_part();
real imaginary_part();
complex reciprocal() const;
complex power( int n ) const;
Compute the:
• exponential function exp(z),
• the natural logarithm ln(1 + z),
where z is this. Use the respective Taylor expansions at 0 (i.e. the
Maclaurin series). The number of terms to use is given by terms.
complex exp( int terms ) const;
complex log1p( int terms ) const;
Compute the absolute value of the given complex number to the given
precision (the argument prec gives the upper bound on the admissible
approximation error). You may find the newton demo from week 2
helpful to compute abs. Don’t forget to find a suitable starting point
for the approximation, otherwise convergence will be very slow.
real abs( real prec = epsilon ) const;
To compute the argument, you will need the inverse tangent (atan),
which can be approximated using its Maclaurin series in the closed
interval ⟨−1, 1⟩. There is only one problem: the convergence near ±1
is very slow. Hence, you want to use a different series here (discovered
by Euler):
∑ 22n
(n!)2
x2n+1
/(2n + 1)!(1 + x2
)n+1
Though this one will eventually converge everywhere, it is particularly
good in the same ⟨−1, 1⟩ interval. In this interval, it can be truncated
at the first term less than half the required precision.
Now note that for any given x, either x or 1/x falls into ⟨−1, 1⟩: hence,
you can use the reciprocal formula (atan(1/x) is 2*atan(1) - atan(x))
to find an expression for the argument which always falls into the
interval of (fast) convergence.
Don’t forget that adding two numbers each with error ≤ ε only guarantees
that the sum has an error ≤ 2ε. Likewise, multiplication by an
exact constant also multiplies the error.
real arg( real prec = epsilon ) const;
Compute the exponential and log1p to a given precision. Assume that
z (this) is in the area of convergence for the required power series (the
open unit disc for log1p, the entire complex plane for exp).
Tip: to judge the precision, use the norm (square of the modulus), not
the modulus itself. For exp, depending on the argument, the terms of
the power series may grow before they start to shrink. Once they start
to shrink and their norm falls below prec squared, you have achieved
the required precision. How things work out with log1p is left as an
exercise (it’s much simpler).
complex exp( real prec = epsilon ) const;
complex log1p( real prec = epsilon ) const;
};
Part T.2.2: [machine]
In this task, you will implement a simple register machine (i.e. a simple
model of a computer). The machine has an arbitrary number of integer
registers and byte-addressed memory. Registers are indexed from 1
to INT_MAX. Each instruction takes 2 register numbers (indices) and an
‘immediate’ value (an integral constant). Each register can hold a single
value of type int32_t (i.e. the size of the machine word is 4 bytes).
In memory, words are stored LSB-first. The entire memory and all
registers start out as 0.
The machine has the following instructions (whenever reg_x is used in
the description, it means the register itself (its value or storage location),
not its index; the opposite holds in the column reg_2 which always
refers to the register index).
opcode reg_2 description
mov ≥ 1 copy a value from reg_2 to reg_1
= 0 set reg_1 to immediate
add ≥ 1 store reg_1 + reg_2 in reg_1
= 0 add immediate to reg_1
mul ≥ 1 store reg_1 * reg_2 in reg_1
jmp = 0 jump to the address stored in reg_1
≥ 1 jump to reg_1 if reg_2 is nonzero
load ≥ 1 copy value from addr. reg_2 into reg_1
stor ≥ 1 copy reg_1 to memory address reg_2
halt = 0 halt the machine with result reg_1
≥ 1 same, but only if reg_2 is nonzero
Each instruction is stored in memory as 4 words (addresses increase
from left to right). Executing a non-jump instruction increments the
program counter by 4 words.
reg_2reg_1immediateopcode
enum class opcode { mov, add, mul, jmp, load, stor, hlt };
class machine
{
public:
Read and write memory, one word at a time.
int32_t get( int32_t addr ) const;
void set( int32_t addr, int32_t v );
Start executing the program, starting from address zero. Return the
value of reg_1 given to the hlt instruction which halted the computa-
tion.
int32_t run();
};
Part T.2.3: [natural]
In this task, you will implement a class which represents arbitrary-size
natural numbers (including 0). In addition to the methods prescribed
PB161 Programming in C++ 61/114 June 28, 2022
below, the class must support the following:
• arithmetic operators +, -, *, / and % (the last two implementing division
and reminder),
• all relational operators,
• bitwise operators ^ (xor), & (and) and | (or).
The usual preconditions apply (divisors are not 0, the second operand
of subtraction is not greater than the first).
class natural
{
public:
Construct a natural number, optionally from an integer. Throw
std::out_of_range if v is negative.
explicit natural( int v = 0 );
natural power( natural exponent ) const;
natural digit_count( natural base ) const;
natural digit_sum( natural base ) const;
};
Part T.2.4: [parser]
Write a parser for simplified JSON: in our version, object keys are
barewords (i.e. there is no escaping to deal with) and values are integers,
arrays or objects (no strings or floats). The EBNF:
(* toplevel elements *)
value = blank, ( integer | array | object ), blank ;
integer = [ '-' ], digits | '0' ;
array = '[', valist, ']' | '[]' ;
object = '{', kvlist, '}' | '{}' ;
(* compound data *)
valist = value, { ',', value } ;
kvlist = kvpair, { ',', kvpair } ;
kvpair = blank, key, blank, ':', value ;
(* lexemes *)
digits = nonzero, { digit } ;
nonzero = '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' ;
digit = '0' | nonzero ;
key = keychar, { keychar } ;
keychar = ? ASCII upper- or lower-case alphabetical character ? ;
blank = { ? ASCII space, tab or newline character ? } ;
It is okay to use std::isspace to implement the blank nonterminal. The
interface should be as follows:
class json_value;
using json_ptr = std::unique_ptr< json_value >;
using json_ref = const json_value &;
enum class json_type { integer, array, object };
class json_error
{
public:
const char *what() const;
};
class json_value
{
public:
virtual json_type type() const = 0;
virtual int int_value() const = 0;
virtual json_ref item_at( int ) const = 0;
virtual json_ref item_at( const std::string & ) const = 0;
virtual int length() const = 0;
virtual ~json_value();
};
Semantic requirements:
• when a string that is passed to json_parse does not conform to the
above grammar, the function should throw an exception of type
json_error,
• a duplicated key within an object should throw json_error too,
• the item_at overloads should throw an instance of
std::out_of_range when the specified element does not exist,
• the item_at overload which accepts an integer, when called on a
value of type json_type::object, should return elements in keyalphabetical
order,
• length should never throw (integers should have a length of 0).
Check that the input document is well-formed (i.e. it conforms to the
grammar). Return true or false depending on the outcome. Do not
throw any exceptions.
bool json_validate( const std::string & );
Read a simplified-JSON document. Throw json_error if the document
is ill-formed.
json_ptr json_parse( const std::string & );
Part 9: Templates
You have hopefully already noticed that certain classes in the C++ standard
library are parametric: they can be instantiated with different
type parameters: that is, we can create an std::vector of integers, but
we can also create an std::vector of floating-point numbers. Even
more interestingly, we can create an std::vector of instances of our
own classes. It is probably quite clear that there is a single entity called
std::vector: this entity is called a class template. Unfortunately, the
terminology gets slightly confusing here: the instances of class templates
are classes. This is different from objects which are also known
as class instances.
Demonstrations:
1. zipper – our favourite data structure, now generic
2. expr – a different take on expressions
3. fold – function templates
4. rel – non-type template arguments
Elementary exercises:
1. iota – generate an integer sequence
2. quot – quotient fields (aka fields of fractions)
3. split – slice a string view into two on a delimiter
Preparatory exercises:
1. circular – a circular list, but generic
2. buffer – a fixed-size queue-like data structure
3. stats – median, quartiles, mode over any container
4. sparse – sparse copy-on-write arrays
5. bbox – a bounding box of a point collection
6. visit – call a function on each node of a graph
Regular exercises:
1. tfold – fold a tree using an arbitrary function
2. tmap – apply a function to each node
PB161 Programming in C++ 62/114 June 28, 2022
3. monoid – free monoids and homomorphisms
4. treap † – a combination of a heap and a binary search tree
5. critbit – binary tries with generic values
6. finally – a generic RAII wrapper
Part 9.d: Demonstrations
9.d.1 [zipper] The canonic use for C++ templates is designing container
classes (collections) which can hold different types of values. In C, the
solution was to either use void pointers (e.g. linked lists in PB071),
implement data structures using macros (e.g. linked lists in the Linux
kernel), or remember store sizes explicitly and copy in data using void
pointers and the element size (e.g. glib data structures). Let’s now
look at the C++ way, using the familiar zipper as an example. You
may find it helpful to compare this example with 05/access.cpp, which
implemented a non-generic version of the same class.
Definition of a class template looks the same as a definition of a normal
class, all we need to do is specify that we want a template instead, with
a single type parameter, which is, by convention, called T:
template< typename T >
We can now proceed to define a class and it will become a class template
(i.e. it will be parametrized by T above). Anywhere in the body of
the class where we can specify a type, we can now also use T. When
we instantiate the template later, the compiler will find all occurrences
of T in the class definition and replace them with the supplied type
parameter. This process is known as substitution.
class zipper
{
If you remember from a few weeks ago, a zipper can be represented
using 2 stacks. Like before, we will use a pair of std::vector instances.
However, the zipper now stores values of type T, so we will supply that
as the type parameter of vector.
using stack = std::vector< T >;
stack left, right;
T focus;
public:
Forwarding arguments of arbitrary types is a little too advanced for
us, so we will settle for making a copy of the initial value. This means
that we require T to be a type with a copy constructor. In other words,
we won’t be able to create zippers that hold values of type unique_ptr.
zipper( const T &f ) : focus( f ) {}
Like above, we will settle for a copy.
zipper &push_left( const T &x )
{
left.push_back( x );
return *this;
}
zipper &push_right( const T &x )
{
right.push_back( x );
return *this;
}
The shift helper remains unchanged from our previous implementa-
tion.
void shift( stack &a, stack &b )
{
b.push_back( focus );
focus = a.back();
a.pop_back();
}
This time, we will only have pre-increment and pre-decrement, since
those are the only practical variants for this class.
zipper &operator++() { shift( right, left ); return *this; }
zipper &operator--() { shift( left, right ); return *this; }
The dereference and indirect access operators are more interesting,
since they need to mention the element type, which is now T.
T &operator*() { return focus; }
T *operator->() { return &focus; }
And the const overloads of the same:
const T &operator*() const { return focus; }
const T *operator->() const { return &focus; }
Indexing operator (non-const overload only).
T &operator[]( int i )
{
if ( i == 0 ) return focus;
if ( i < 0 ) return left[ left.size() + i ];
if ( i > 0 ) return right[ right.size() - i ];
assert( false );
}
};
int main() /* demo */
{
Let’s first create a zipper which holds integers.
zipper< int > zi( 0 ); // [0]
zi.push_left( 2 ); // 2 [0]
zi.push_left( 1 ); // 2 1 [0]
zi.push_right( 1 ); // 2 1 [0] 1
check
assert( zi[ -2 ] == 2 );
assert( zi[ -1 ] == 1 );
assert( zi[ 0 ] == 0 );
assert( zi[ 1 ] == 1 );
assert( *zi == 0 );
And now a different instance, with pairs.
using p = std::pair< int, int >;
zipper< p > zp( p( 0, 1 ) );
assert( *zp == p( 0, 1 ) );
assert( zp->first == 0 );
assert( zp->second == 1 );
zp.push_left( p( 7, 7 ) );
assert( zp[ -1 ] == p( 7, 7 ) );
-- zp;
assert( zp->first == 7 );
assert( zp->second == 7 );
}
9.d.2 [expr] We will do another take at expressions, this time with templates,
which will allow us to use values instead of references. While
the first two examples were directly comparable to earlier versions,
this one will deviate quite far from 07/expr.cpp, though you may still
find it useful to quickly go over that one first. The semantics will be
the same: we will have sums, products and constants. However, there
PB161 Programming in C++ 63/114 June 28, 2022
will be no distinction between static and dynamic types and no virtual
methods.
We will start with constants, since those are the simplest. Since we are
not using virtual methods, we also don’t need a common base class or
inheritance. We do, however, need to provide a common interface (i.e.
method names and signatures) between the different classes.
class constant
{
int _value;
public:
constant( int v ) : _value( v ) {}
int value() const { return _value; }
};
So far, we have only seen templates with a single type parameter. However,
we can have as many as we want (in fact, we can even have a
variable number, though that is outside of the scope of this subject). For
sum, we will need 2: the type of the left and of the right sub-expression.
template< typename left_t, typename right_t >
class sum
{
Unlike before, the static type of the left and the right sub-expressions
may be different, and instead of references or pointers, we will simply
store them by value in attributes.
left_t _left;
right_t _right;
public:
We need to define a constructor. Like in our earlier take on expressions,
the constructor will take the two sub-expressions as arguments. This
time, their types are given by the template parameters though. Other
than that, the constructor is pretty normal.
sum( const left_t &l, const right_t &r )
: _left( l ), _right( r )
{}
And the interface to get values out of the expression:
int value() const { return _left.value() + _right.value(); }
};
The product class looks pretty much the same:
template< typename left_t, typename right_t >
class product
{
left_t _left;
right_t _right;
public:
product( const left_t &l, const right_t &r )
: _left( l ), _right( r )
{}
int value() const { return _left.value() * _right.value(); }
};
The duplication is somewhat unsatisfactory. Maybe we could do a little
better by using inheritance, so let’s try defining another class. First
the base class:
template< typename left_t, typename right_t >
class operation
{
protected:
left_t _left;
right_t _right;
public:
operation( const left_t &l, const right_t &r )
: _left( l ), _right( r )
{}
};
Now a derived class – let’s do subtraction. Remember that inheritance
works with classes, but operation is a class template: we need to instantiate
it to obtain a class before we can inherit from it!
template< typename left_t, typename right_t >
class difference : public operation< left_t, right_t >
{
public:
difference( const left_t &l, const right_t &r )
: operation< left_t, right_t >( l, r ) {}
Plot twist: if the type of the base class depends on template parameters,
we cannot directly access inherited attributes. Instead, we have to
explicitly tell the compiler that those are attributes of this class using
this.
int value() const
{
return this->_left.value() - this->_right.value();
}
};
That wasn’t much better. Templates are, unfortunately, somewhat
verbose. On the upside, notice that we have implemented the first
two operations (+, *) somewhat differently from the last (-), but they
can still interoperate smoothly. Templates use duck typing: if it looks
and quacks like a duck (i.e. it has the right attributes and methods) it
probably is a duck, and the compiler will let us use the type with the
template.
int main() /* demo */
{
We first define some constants, those are simple.
constant c_0( 0 ), c_1( 1 ), c_2( 2 );
When we create instances of class templates using constructors which
take arguments of types that match the type parameters of the template,
we do not need to explicitly type them out. This is the same
principle that lets us write std::pair( 0, 1 ). The feature is called template
argument deduction and we will see more of it with function
templates in the next unit. Of course, we can specify the template
arguments ourselves if we want to, but it gets tedious rather quickly.
We will show both styles, first the explicit one:
sum< constant, constant > s_1( c_0, c_1 );
sum< sum< constant, constant >, constant > s_2( s_1, c_1 );
This is clearly impractical. Let’s try the implicit style.
sum s_3( s_2, c_1 );
product p_0( c_0, c_1 );
product p_1( c_1, s_1 );
That is much better. Let’s make some differences and then we will
check all the values.
difference d_2( s_3, s_1 );
difference d_0( d_2, c_2 );
assert( c_0.value() == 0 );
assert( s_1.value() == 1 );
assert( s_2.value() == 2 );
assert( s_3.value() == 3 );
assert( p_0.value() == 0 );
assert( p_1.value() == 1 );
PB161 Programming in C++ 64/114 June 28, 2022
assert( d_2.value() == 2 );
assert( d_0.value() == 0 );
}
9.d.3 [fold] In this unit, we will look at function templates, which are
similar to class templates we have seen in previous units. Function
templates rely even more heavily on template parameter deduction
than class templates: most of the time, calling function templates looks
just like calling standard function: the compiler will deduce the type
parameters from the actual argument types. We will see that later
down.
One further thing to note is that we have actually met function templates
quite early on, we just did not mention they were templates: the
call operator of a lambda with an auto parameter is, in fact, a function
template, the only difference is that the syntax is (usually) less verbose.
We will start by defining some commonly useful folds on containers.
Let’s start with sum. The container type will be a type parameter: we
want our sum to work on different container types (for instance sets
and vectors) and also with different element types: the types of items
stored in those containers. The syntax for function templates is pretty
much the same as it was for class templates:
template< typename container_t >
followed by a standard function signature. In this case, we have a
small problem, since we don’t have a name for the type of the return
value. For now, we can use auto.
auto sum( const container_t &xs )
{
There are two ways to go about writing the summing loop, with different
trade-offs in terms of types. Probably the most reasonable thing
to do is to declare an accumulator of the correct type and initialize it
to 0. For that, however, we need to know the type of the values stored
in xs. Fortunately, standard library provides us with a way to do just
that: each standard container has a nested type name, which we can
access using ::. If the outer type is a template argument, or depends
on a template argument, we additionally need to tell the compiler that
we intend to refer to a type (since templates are duck typed, the nested
name could also turn out to be an attribute or a method). The type of
a single element stored in a container is known as its value_type.
using value_t = typename container_t::value_type;
Now that we have named the type of values in the container, we can
declare an accumulator with the correct type. Again, by the virtue of
duck typing, we do not know for certain whether values of this type
can be constructed from integers, but we assume that they can. When
we attempt to use the template, the compiler will check and emit errors
if this is, in fact, not possible.
value_t accum = 0;
The loop itself is then quite trivial.
for ( const auto &x : xs )
accum = accum + x;
return accum;
}
Let’s also try to do a product, in a slightly different style, just to see
some more options. In this case, since we do not make any use of
container_t, it would be easier to simply use a lambda. We will do that
in a bit.
template< typename container_t >
auto product( const container_t &xs )
{
auto accum = xs.empty() ? 1 : *xs.begin();
bool first = true;
for ( const auto &x : xs )
if ( first )
first = false;
else
accum = accum * x;
return accum;
}
Let us do mean in a lambda style, so we have a comparison at hand.
We can re-use sum from above. We will take the average of an empty
sequence to be 0.
static auto mean = []( const auto &xs )
{
return xs.empty() ? 0 : sum( xs ) / xs.size();
};
Finally, we will generalize the two folds (sum and product), and add
a zip_with for a good measure, in the template style. We can accept
functions as arguments the same way we accept any other values. This
will work with anything that can be called (remember duck typing?),
most importantly lambdas.
The initial value of the accumulator passed in by the user gives us the
type of the accumulator ‘for free’. In practice, this is a little dangerous
in the sense that it could give us some unexpected results if enough
implicit conversions are allowed (like accumulating rational numbers
into an integer). I will show you another version of fold as a bonus
after we do zip_with.
template< typename xs_t, typename fun_t, typename init_t >
auto fold( const xs_t &xs, const fun_t &f, const init_t &init )
{
The fold itself is pretty trivial, once we have figured out the types.
init_t accum = init;
for ( const auto &x : xs )
accum = f( accum, x );
return accum;
}
Now for the zip_with. It will accept two sequences and a function. The
result will be a vector, since we do not have a good way to tell the
function what type of a container we would like.
template< typename xs_t, typename ys_t, typename fun_t >
auto zip_with( const xs_t &xs, const ys_t &ys, const fun_t &f )
{
We need a new trick, because there is nothing at hand that would give
us the element type of the result (even if we settled for a vector as
the container). The way to find out is decltype, an operator that takes
an expression and produces its type. Whenever we can write out a
name of a type, we can instead use decltype with an expression. The
expression must only refer to names that are in scope at the point of
the decltype though.
using value_t = decltype( f( *xs.begin(), *ys.begin() ) );
Note: there is a bit of a danger in the above: this function will not work
with an f that returns a reference. Repairing this deficiency is beyond
the scope of this course. Ask if you are interested though.
std::vector< value_t > out;
We want our zip_with to terminate when it hits the end of the shorter
sequence. This means we cannot use std::transform, unfortunately,
so we will type out the loop by hand.
PB161 Programming in C++ 65/114 June 28, 2022
auto x = xs.begin();
auto y = ys.begin();
while ( x != xs.end() && y != ys.end() )
out.push_back( f( *x++, *y++ ) );
return out;
}
And finally, the promised ‘bonus’ fold, which prefers the return type of
f as its accumulator type. We have the basic recipe for that in zip_with.
template< typename xs_t, typename fun_t, typename init_t >
auto fold_( const xs_t &xs, const fun_t &f, const init_t &init )
{
using accum_t = decltype( f( init, *xs.begin() ) );
Note that accum_t and init_t may be different types.
accum_t accum = init;
for ( const auto &x : xs )
accum = f( accum, x );
return accum;
}
For a good measure, we will define a custom class of numbers. You
might remember rat from an earlier exercise. The minimum viable
definition follows.
struct rat
{
int p, q;
rat( int p, int q = 1 ) : p( p ), q( q ) {}
friend rat operator+( rat r, rat s )
{
return { r.p * s.q + s.p * r.q, r.q * s.q };
}
rat operator*( rat r ) const { return { p * r.p, q * r.q }; }
rat operator/( rat r ) const { return { p * r.q, q * r.p }; }
bool operator<( rat r ) const { return p * r.q < r.p * q; }
bool operator==( rat r ) const { return p * r.q == r.p * q; }
};
int main() /* demo */
{
std::set< int > xs{ 1, 2, 3 };
std::vector< double > ys{ 1.5, 2 };
std::set< rat > zs{ 1, { 1, 2 }, { 1, 4 } };
The only interesting thing in the below test cases is that the functions
are used like standard functions: no angle brackets to be seen anywhere.
This is because the compiler deduces the type parameters from
the types of the actual arguments which we pass into the function.
Since all template arguments can be deduced this way, we can omit
angle brackets entirely.
assert( sum( xs ) == 6 );
assert( sum( ys ) == 3.5 );
assert( sum( zs ) == rat( 7, 4 ) );
assert( product( xs ) == 6 );
assert( product( ys ) == 3 );
assert( product( zs ) == rat( 1, 8 ) );
assert( mean( xs ) == 2 );
assert( mean( ys ) == 1.75 );
assert( mean( zs ) == rat( 7, 12 ) );
When calling our original fold, we have to be careful with the type of
the initial value, otherwise we will run into problems. This is somewhat
inconvenient.
assert( fold( zs, std::plus<>(), rat( 0 ) ) == rat( 7, 4 ) );
On the other hand, our improved version (here named fold_) works
just fine if we write it in a ‘natural’ style.
assert( fold_( zs, std::plus<>(), 0 ) == rat( 7, 4 ) );
Finally, let’s look at zip_with.
std::vector xs_ys{ 2.5, 4.0 };
The sets are sorted in ascending order, so the pairings will be 1/4 + 1,
1/2 + 2 and 1 + 3.
std::vector xs_zs{ rat( 5, 4 ), rat( 5, 2 ), rat( 4 ) };
assert( zip_with( xs, ys, std::plus<>() ) == xs_ys );
assert( zip_with( xs, zs, std::plus<>() ) == xs_zs );
}
9.d.4 [rel] We will take a second look at function templates, but this
time we will also add non-type template arguments to the mix. We
haven’t used it much, but this is how std::get works. It might be useful
to review 03/p4_rel.cpp before diving into this example.
General projections are still too hard for us, so we will only do a singlecolumn
projection. However, selection is easier so let’s look at those
first. We will need 3 template arguments: one to specify which column
to use as the selection criterion, another to specify the type of a single
row and the last one to specify the type of the value which we will
compare with the entries.
template< int index, typename rel_t, typename key_t >
rel_t select( const rel_t &rel, const key_t &key )
{
Since the type of the relation does not change under selection, it is
simple enough to create an empty relation and add matching rows
from rel to it.
rel_t out;
We assume that it is possible to iterate a rel_t, and that it is possible to
insert things into a rel_t. Since templates are duck-typed, this will be
checked when the template is instantiated.
for ( const auto &row : rel )
We now need to decide whether the row matches the criterion: the
index-th column should be equal to key for that, so let’s check that.
if ( std::get< index >( row ) == key )
Just insert the row.
out.insert( row );
And return the result.
return out;
}
Now for a single-column projection. Again, we will pass in index as a
template parameter. However, we will run into some problems with
the return type. Fortunately, in the signature, we can just use auto as
the return type and worry about it later.
template< int index, typename rel_t >
auto project( const rel_t &rel )
{
Actually, we can’t put that off for very long. We need to declare the
variable to hold the resulting relation. First of all, we need to find out
PB161 Programming in C++ 66/114 June 28, 2022
the type of a single row. For that, we can use standardized nested
types that all std containers provide, which we have learned about
in the previous unit. The row is the value_type of the relation, like
this. Remember that the typename specifier is compulsory whenever
we want to refer to a type nested within a template parameter, or
within something that depends on a template parameter.
using row_t = typename rel_t::value_type;
Now that we have the row type, we need to extract the type of index-th
column. For that, the standard library provides the tuple_element_t
helper template, like this:
using col_t = std::tuple_element_t< index, row_t >;
Now we have the type that we need to construct the output relation,
which we will construct as a set of col_t.
std::set< col_t > out;
At this point, the code for project is just a variation on what we already
saw in select.
for ( const auto &row : rel )
out.insert( std::get< index >( row ) );
return out;
}
int main() /* demo */
{
using element = std::tuple< std::string, int, double >;
using elem_rel = std::set< element >;
We first define a testing data set.
elem_rel r{ { "hydrogen", 1, 0.78 },
{ "hydrogen", 2, 1.50 },
{ "hydrogen", 3, 3.09 },
{ "helium", 3, 3.09 },
{ "iron", 56, 9.15 },
{ "iron", 58, 9.14 },
{ "nickel", 60, 9.15 },
{ "nickel", 62, 9.15 } };
Using select is straightforward: we specify, as a template parameter
(i.e. using angle brackets) the column index, and pass in the relation
and the key as standard arguments. The types of the relation and the
key are then deduced automatically. You may find it helpful to compare
the calls with the definition of select above.
elem_rel nickel = select< 0 >( r, "nickel" ),
iron = select< 0 >( r, "iron" ),
helium = select< 0 >( r, "helium" );
elem_rel helium_expect{ { "helium", 3, 3.09 } },
iron_expect { { "iron", 56, 9.15 },
{ "iron", 58, 9.14 } },
nickel_expect{ { "nickel", 60, 9.15 },
{ "nickel", 62, 9.15 } };
assert( helium == helium_expect );
assert( iron == iron_expect );
assert( nickel == nickel_expect );
Now for projection: again, we explicitly specify the index of the column
to extract, as a template parameter. The type of the relation is deduced
and we therefore do not need to mention it.
auto names = project< 0 >( r );
std::set< std::string > names_expect{ "hydrogen", "helium",
"iron", "nickel" };
assert( names == names_expect );
std::set< std::pair< int, int > > p{ { 1, 1 }, { 1, 2 },
{ 2, 2 }, { 2, 4 } };
std::set< int > left{ 1, 2 }, right{ 1, 2, 4 };
assert( project< 0 >( p ) == left );
assert( project< 1 >( p ) == right );
assert( project< 1 >( select< 0 >( p, 1 ) ) == left );
}
Part 9.e: Elementary Exercises
9.e.1 [iota] Implement a generic function iota, which, given a function
f, calls f( start ), f( start + 1 ), … f( end - 1 ), in this order.
// void iota( … f, int start, int end );
9.e.2 [quot] A quotient field is a generalization of rational numbers:
one can be constructed from any integral domain. When the integral
domain is taken to be Z (the integers), the result is Q (the rational
numbers). However, the construction is much more general and can
be applied to polynomials, Gaussian integers, p-adic numbers and so
on. Here, we will construct standard rationals and Gaussian rationals
(which are like normal rationals, but with an imaginary part).
Define a class template rat. The type parameter will provide the integral
domain: int for integers, gauss for Gaussian integers. The constructor
should take the numerator and the denominator as arguments.
Define addition, multiplication and division on rat’s, as well as equality.
When done, implement gauss, which is simply a complex number
where both the real and imaginary parts are integers. Store them
in algebraic form for simplicity. Define addition, multiplication and
equality.
9.e.3 [split] Implement a function split, which given a string view
s and a delimiter delim, produces a pair of string_views a and b such
that:
• delim is not in a,
• and either
∘ s == a + delim + b if delim was present in s,
∘ s == a and b is empty otherwise
using split_view = std::pair< std::string_view, std::string_view >;
split_view split( std::string_view s, char delim );
Part 9.p: Preparatory Exercises
9.p.1 [circular] In this exercise, we will implement a circular list again,
but this time generically, i.e. using templates. Like before, instead of
the usual access operators and iteration, it will have a rotate method,
which rotates the entire list. We require that rotation does not invalidate
any references to elements in the list.
If you think of the list as a stack, you can think of the rotate operation
as taking an element off the top and putting it at the bottom of the
stack. It is undefined on an empty list.
To add and remove elements, we will implement push and pop which
work in a stack-like manner. Only the top element is accessible, via
the top method. This method should allow both read and write access.
Finally, we also want to be able to check whether the list is empty. It is
okay to make copies in push, but make sure you return references in
top.
template< typename T >
struct circular_node; /* ref: 8 lines */
template< typename >
class circular; /* ref: 34 lines */
PB161 Programming in C++ 67/114 June 28, 2022
9.p.2 [buffer] We will implement another data structure. We have
not demonstrated the use of non-type template parameters with class
template, but the principle is the same as it was in function templates in
d4_rel.cpp. An additional hint: the size of an std::array is a non-type
template argument (of type size_t).
Implement a bounded circular buffer with a fixed size, as a class template
with a single type argument T (which comes first) and a single
non-type argument size of type size_t (which comes second). The
class should be default-constructible and it can assume that T is also
default-constructible and that it can be copied. The circular buffer
should provide the following methods:
• push inserts a value at one ‘end’
• pop removes and returns a value from the other ‘end’
• empty which returns true if there are no items
• full if there are already size items
Calling push on a full and pop on an empty buffer is undefined. Pushing
new items should wrap around the end of the storage and start re-using
storage from the start, as long as pop has been called in the meantime
(i.e. the buffer is not full). In other words, buffer with push and pop
behave like a FIFO queue which can hold at most size elements.
template< typename T, size_t size >
class buffer; /* ref: 23 lines */
9.p.3 [stats] In this exercise, we will do some basic statistics: median,
quartiles and mode.
Implement the functions mode, median and quartiles, in such a way that
it accepts any sequential std container, with element type that allows
less-than and equality comparison. Additional notes:
• mode returns an std::set of numbers, since there might be arbitrarily
many: include any input number for which the number of
occurrences is maximal
• median return a single number; pick the smaller of the two elements
if the median lies in between two different numbers
• quartiles returns numbers at indices (size / 4) and ( ( 3 * size ) / 4 ) of
the sorted input sequence, in an std::pair [this is slightly incorrect
but simpler].
// mode: ref. 15 lines
// median: ref. 7 lines
// quartiles: ref. 8 lines
9.p.4 [sparse] Imagine there is a large array of data (e.g. numbers),
but we sometimes need to change a few of those. However, we also
need to keep the original data intact, and we don’t want to copy all the
data around. In this exercise, we will design a simple solution to this
problem.
Implement class template sparse, with a type argument T and a size_t
argument N, with the following interface:
• construct from an std::array of T with size N,
• construct a copy (the array given to the constructor is shared by all
copies),
• set( i, v ) replaces the value stored at index i with v (without
affecting the backing array),
• get( i ) returns the value at index i (that is the v passed to latest
call to set( i, v ) with the same i, or the value from the backing
array if set was never called for i,
• merge() that propagates the changes made in this instance into all
other instances sharing the same backing array.
Note: the memory complexity should be O(N) of shared data, and O(M)
per instance of sparse where M is the number of altered indices. A
merge on one copy should not affect altered indices in other copies.
template< typename T, size_t N >
class sparse;
9.p.5 [bbox] We will dust off geometry a little bit: we will look at constructing
a bounding box around a sequence of points (this time in
3D).
Points can be constructed from three floating-point numbers (of type
double.
struct point;
There is a dist function which gives the Euclidean distance of two
points.
double dist( point a, point b );
A helper function to check approximate point equality.
bool close( point a, point b ) { return dist( a, b ) < 1e-10; }
Now for the bounding box: we want an axis-aligned box (i.e. not the
smallest one), and will represent it using 2 points – those in the opposite
corners. Some of the resulting dimensions might be 0 (in case the
points all lie on a line or in a plane). Return the points in such a way
that the coordinates of the first one are smaller along all axes. It should
be possible to pass the points using a const reference to any container
which can be iterated.
using box_t = std::pair< point, point >;
// ... box_t box( ... )
9.p.6 [visit] The input graph is given using adjacency lists: the graph
type gives the successors for each vertex present in the graph.
template< typename vertex_t >
using graph = std::map< vertex_t, std::vector< vertex_t > >;
Visit each vertex of graph g reachable from initial once and call f on
its value. The order of calls is not important.
// void visit( … g, … f, … initial );
Part 9.r: Regular Exercises
9.r.1 [tfold] Fold a proper binary tree using an associative and commutative
binary function (proper meaning that each node either has
both children, or none).
template< typename value_t >
struct tree
{
std::unique_ptr< tree > left, right;
value_t value;
static auto make_tree( const tree &t )
{
return std::make_unique< tree >( t );
}
tree( const tree &t )
: left( t.left ? make_tree( *t.left ) : nullptr ),
right( t.right ? make_tree( *t.right ) : nullptr ),
value( t.value )
{}
tree( value_t value, const tree &l, const tree &r )
: left( make_tree( l ) ),
right( make_tree( r ) ),
value( std::move( value ) )
{}
tree( value_t value ) : value( std::move( value ) ) {}
};
PB161 Programming in C++ 68/114 June 28, 2022
Given a binary function f and a tree instance t, compute a single value
that is the result of folding the entire tree. Since f is both associative
and commutative, it does not matter in which order you combine the
individual values.
// … tfold( … f, … t )
9.r.2 [tmap] Goal: build a tree by preserving the structure of an existing
tree, but obtain new values by applying a given function to the
originals. The type of the value may change. Hint: assuming
• function_t fun is a unary function,
• value_t val is a value such that fun( val ) makes sense,
you can use:
• std::invoke_result_t< function_t, value_t > to obtain the type of
fun( val ) without having either fun or val (only their types).
template< typename value_t >
struct tree
{
value_t value;
std::vector< tree > children;
tree( value_t v, std::vector< tree > ch = {} )
: value( std::move( v ) ), children( std::move( ch ) )
{}
};
Build a tree of a suitable type given a function f which maps values to
values and some tree t, compatible with f.
// … tmap( … f, … t )
9.r.3 [monoid] Monoids are algebraic structures with a single operation,
usually written as multiplication. A free monoid M on a set A is defined
as the set of all strings of elements from A with concatenation as the
operation. A monoid homomorphism is a map f from M to M′ with
the property f(a ⋅ b) = f(a) ⋅ f(b). All monoids arise as homomorphic
images of a free monoid on some set.
Define a class template monoid, which takes a single type argument,
hom_t, with the following behaviour:
• the constructor will then accept hom, a value (typically a lambda) of
type hom_t, as an argument and store it in an attribute (by value),
• method elem, which takes an std::string and returns a value of a
suitable type with a multiplication and an equality operator.
The class should work with a fixed underlying set: the minuscule Latin
letters (i.e. ’a’ through ’z’) and use the mechanics of a free monoid to
implement multiplication. The provided hom will take an std::string
as an argument, and return a value of some arbitrary type. Assume
applying hom to a string yields values which can be compared, but
not multiplied (at least not in a way compatible with the provided
homomorphism).
template< typename hom_t >
class monoid_element; /* ref: 11 lines */
template< typename hom_t >
class monoid; /* ref: 8 lines */
9.r.4 [treap] † A treap is a combination of a binary search tree and
a binary heap. Of course, a single structure cannot be a heap and a
search tree on the same value:
• a search tree demands the value in the right child to be greater than
the value in the root,
• a max heap demands that the value in both children be smaller
than the root (and hence specifically in the right child).
Treap has therefore a pair of values in each node: a key and a priority.
The tree is arranged so that it is a binary search tree with respect to
keys, and a binary heap with respect to priorities.
The role of the heap part of the structure is to keep the tree approximately
balanced. Your task is to implement the insertion algorithm
which works as follows:
1. insert a new node into the tree, based on the key alone, as with a
standard binary search tree,
2. if this violates the heap property, rotate the newly inserted node
toward the root, until the heap property is restored.
The deeper the node is inserted, the more likely it is to violate the heap
property and the more likely it is to bubble up, causing the affected
portion of the tree to be rebalanced by the rotations. Remember that
rotations do not change the in-order of the tree and hence cannot
disturb the search tree property.
The type of the keys is given as a template parameter, while the priority
should be kept as an int. Interface:
• insert( key, priority ) inserts the given values into the tree, maintaining
both invariants,
• root() returns a pointer to the root node (nullptr if the tree is
empty).
Each node then provides the following:
• left() and right() return raw pointers to the left and right child,
or nullptr if the respective child is missing,
• priority() and key() give access to the values stored in the node.
template< typename key_t >
class treap;
template< typename node_t >
void check_heap( const node_t &n )
{
for ( auto child : { n.left(), n.right() } )
if ( child )
{
assert( child->priority() <= n.priority() );
check_heap( *child );
}
}
template< typename node_t >
std::pair< int, int > check_search( const node_t *n, int bound )
{
if ( !n )
return { bound, bound };
auto [ l_min, l_max ] = check_search( n->left(), n->key() );
auto [ r_min, r_max ] = check_search( n->right(), n->key() );
assert( l_max <= n->key() && n->key() <= r_min );
return { l_min, r_max };
}
treap< int > make_treap( int count )
{
std::mt19937 rand( 0 );
std::uniform_int_distribution< int > dist( -10, 1000 );
treap< int > t;
for ( int i = 0; i < count; ++ i )
{
t.insert( dist( rand ), dist( rand ) );
assert( t.root() );
check_search( t.root(), 0 );
check_heap( *t.root() );
}
return t;
PB161 Programming in C++ 69/114 June 28, 2022
}
template< typename node_t >
int get_depth( const node_t &n )
{
int depth = 1;
for ( auto child : { n.left(), n.right() } )
if ( child )
depth = std::max( depth, get_depth( *child ) );
return depth;
}
void check_sized( int size )
{
double depth_sum = 0;
const int count = 100;
for ( int i = 0; i < count; ++i )
{
auto t = make_treap( count );
depth_sum += get_depth( *t.root() );
}
assert( depth_sum / count <= 2 * ( log2( size ) + 1 ) );
}
9.r.5 [finally] Unlike many other languages, there is no built-in finally
in C++. In this exercise, we will implement a RAII class that
provides similar functionality. The user should be able to write code
like this:
finally close_fd( []{ ::close( fd ); } );
While the syntax is not perfect, it presents some opportunities not
normally available with finally. One is that the guard can be disabled
(add a cancel method to do that) and possibly moved around (e.g. passed
down to a tail call).
Do note that there are pitfalls associated with this kind of object that
we will not be addressing in this exercise. Most importantly, we will
assume that the function passed into finally does not itself throw (if
it does, things will go very badly).
template< typename handler_t >
class finally;
Part 10: Templates (cont’d)
This week, we will practice templates some more, and introduce a
few more useful template constructs. Among other things, we’ll look
at more complicated cases of template argument deduction and how
function overloading interacts with function templates. We will also
look at templated operator overloads.
Demonstrations:
1. apply – call functions on scalars in composite data
2. method – method templates
3. expr – expressions, this time with operator overloading
4. set – operators on sets (with arbitrary element types)
5. call – overloading the call operator
Elementary exercises:
1. format – format collections
2. concat – splice two sequences into one
3. icons – integer lists with compile-time recursion
Preparatory exercises:
1. post – post-order on a generic graph
2. cons – heterogeneous lists
3. map – more template argument deduction
4. collect – extract values from containers
5. list – linked lists with sub-list sharing
6. vecset – implement a set using a sorted vector
Regular exercises:
1. select – create a vector of variants
2. sorted – a stateful sequence observer
3. fsm – generic finite state machines
4. tree – trees with sub-tree sharing
5. bimap – map 2 types of keys to each other
6. tinyvec † – a generic vector in fixed memory
Part 10.d: Demonstrations
10.d.1 [apply] In this example, we will show how to use recursion
together with templates to walk through composite, templated data
types. In particular, we will look at finding and summing up numeric
data types in a binary tree made of std::tuple instances.
We will need a data type to stop the recursive data definitions: an
empty tree, if you will. We will call it null (not to be confused with the
C macro NULL nor with C++ nullptr. We want this to be a unique data
type, but it does not need to carry any actual data, hence we can use
an empty struct.
struct null {};
The summation will be defined recursively, so let’s first define the
overload for the base type: null. The neutral element of addition is 0,
so let’s use 0 as the value of an empty subtree.
int sum( null ) { return 0; }
Now for the non-empty subtrees: we will use 3-tuples: the value in
the node (integer) and the left and right subtrees. We will use template
argument deduction to obtain the type of the composite tuple. Recall
that we used to write function templates somewhat like this:
template< typename T >
int sum( const T &tup )
{
int v = std::get< 0 >( tup );
// ...
}
This is not optimal, because there is a conflict with the null overload
above: the template can be instantiated with T = null. The compiler
will prefer the non-template version (or rather the most specific version),
but the rules are complex and error-prone. It is better to not rely
on those rules if they can be easily avoided.
In this case, we can use a more specific (non-overlapping) overload,
which will only accept 3-tuples. There is no chance that a null is confused
for a 3-tuple. Nonetheless, we still need to figure out how to
do template argument deduction in this case. Easier shown than described.
We will use 2 template type parameters, for the left and right
subtree.
template< typename L, typename R >
However, we cannot directly use L and R as function arguments: we
want to accept 3-tuples. Fortunately, the compiler can also deduce
parts of an argument type:
PB161 Programming in C++ 70/114 June 28, 2022
int sum( const std::tuple< int, L, R > &tup )
{
We can also use structured bindings to decompose the tuple, making
the code easier to read:
const auto &[ v, left, right ] = tup;
The rest of the function now looks like the most straightforward recursive
definition from IB015.
return v + sum( left ) + sum( right );
}
int main() /* demo */
{
std::tuple a{ 3, null(), null() };
std::tuple b{ 7, null(), null() };
std::tuple c{ 1, null(), null() };
std::tuple d{ 10, a, null() };
std::tuple e{ 2, b, c };
std::tuple f{ 0, d, e };
assert( sum( null() ) == 0 );
assert( sum( a ) == 3 );
assert( sum( b ) == 7 );
assert( sum( c ) == 1 );
assert( sum( d ) == 13 );
assert( sum( e ) == 10 );
assert( sum( f ) == 23 );
}
10.d.2 [method] We already know that we can write class templates
and function templates. It is only logical that we can also create method
templates in C++ classes and in class templates.
This example will be somewhat synthetic: we will have a class which
does not permit direct access to its elements, but allows them to be
folded using a function object.
template< typename T >
class foldable
{
std::vector< T > data;
public:
A method to add elements to the internal container.
void push( const T &t ) { data.push_back( t ); }
And the method template to accumulate the content using a function
object.
template< typename fun_t, typename init_t >
init_t fold( const fun_t &fun, init_t init )
{
for ( const auto &e : data )
init = fun( init, e );
return init;
}
};
int main() /* demo */
{
foldable< int > f;
f.push( 7 );
f.push( 3 );
assert( f.fold( std::plus<>(), 0 ) == 10 );
f.push( 10 );
assert( f.fold( std::multiplies<>(), 1 ) == 210 );
}
10.d.3 [expr] This example will demonstrate operator overloading in
conjunction with class templates. Again, we will use argument deduction
with partial types in function signatures, to match the desired
types closely enough to to avoid ambiguities. You can probably imagine
than an operator + that accept arbitrary types as arguments would
not mesh very well with the rest of the program.
First, we will define an enum to tag expressions with the operator they
represent, and a constant class to use as leaf nodes.
enum class expr_op { add, mul };
Constants will be a straightforward class with an eval method, common
with the expr class template below:
struct constant
{
int v;
int eval() const { return v; }
constant( int v ) : v( v ) {}
};
We will start by defining an expr class template.
template< typename left_t, typename right_t >
struct expr
{
expr_op op;
left_t left;
right_t right;
expr( expr_op op, const left_t &l, const right_t &r )
: op( op ), left( l ), right( r )
{}
Compute the value of this node.
int eval() const
{
int l = left.eval(),
r = right.eval();
switch ( op )
{
case expr_op::add: return l + r;
case expr_op::mul: return l * r;
}
assert( false );
}
Like with normal operator overloading, there are multiple ways to
overload operators for class templates. Let’s start by defining a method.
However, we immediately run into a problem: the right operand does
not have to be of the same type as the left one, even though we want it
to be an instance of the same class template. For that reason, we need
to define the operator as a template method.
template< typename l2_t, typename r2_t >
The return type is mildly infuriating, because it needs to spell out the
composite instance. Next time, we will just use auto.
expr< expr< left_t, right_t >, expr< l2_t, r2_t > >
Now for the signature of the operator itself:
operator+( const expr< l2_t, r2_t > &o ) const
{
Now that we have spelled out the monster types, the implementation
is trivial.
return { expr_op::add, *this, o };
}
PB161 Programming in C++ 71/114 June 28, 2022
Now let’s try a friend definition. The gist is the same, and you may
remember that we can still use expr without arguments to mean the
instance with left_t = left_t and right_t = right_t. Then:
template< typename l2_t, typename r2_t >
friend auto operator*( const expr &a,
const expr< l2_t, r2_t > & b )
{
But now we have a problem again. We are in the definition of a class
template, and hence using the name of the class template without
arguments means this specific instance. But we want to construct a
different instance, but using template argument deduction. We need
to tell the compiler that is what we mean by using a qualified name
for the class template: if qualified, the name no longer refers to this
instance.
return ::expr( expr_op::mul, a, b );
}
That covers the expression + expression cases. But we also need to be
able to work with constant instances here. More operators!
friend auto operator+( constant c, const expr &a )
{
return ::expr( expr_op::add, c, a );
}
friend auto operator+( const expr &a, constant c )
{
return ::expr( expr_op::add, a, c );
}
friend auto operator*( constant c, const expr &a )
{
return ::expr{ expr_op::mul, c, a };
}
friend auto operator*( const expr &a, constant c )
{
return ::expr( expr_op::mul, a, c );
}
};
That’s not the end yet. We also need to be able to multiply and add two
constants, to get a complete set. Since the result is an expr instance, it
does not make much sense to put those into the constant class itself.
Let’s use toplevel definitions for those. Fortunately, in this case, the
operators are not templates at least.
auto operator+( constant a, constant b )
{
return expr( expr_op::add, a, b );
}
auto operator*( constant a, constant b )
{
return expr( expr_op::mul, a, b );
}
int main() /* demo */
{
constant a( 1 );
constant b( 2 );
auto c = a + b;
assert( c.eval() == 3 );
assert( ( a * c ).eval() == 3 );
assert( ( a + c ).eval() == 4 );
assert( ( c + c ).eval() == 6 );
}
10.d.4 [set] In which we will combine operator templates and template
argument deduction to spice up the standard std::set container.
We have already seen in apply.cpp that the compiler can deduce template
arguments based on (self-contained) fragments of function argument
types. We will use that along with operator templates to provide
overloads for all instances of std::set, without affecting any other
standard container, or any other type at all.
We will overload operator & for intersection, operator | for union, - for
standard difference and finally ^ for symmetric difference of two sets.
Please keep in mind that the priorities of bitwise operators in C++ are
unintuitive at best: overloaded operators inherit both their priority
and associativity from the built-in ones.
template< typename T >
std::set< T > operator&( const std::set< T > &a,
const std::set< T > &b )
{
std::set< T > out;
Remember standard algorithms?
std::set_intersection( a.begin(), a.end(),
b.begin(), b.end(),
std::inserter( out, out.begin() ) );
return out;
}
Now the union.
template< typename T >
std::set< T > operator|( const std::set< T > &a,
const std::set< T > &b )
{
std::set< T > out;
std::set_union( a.begin(), a.end(),
b.begin(), b.end(),
std::inserter( out, out.begin() ) );
return out;
}
And difference. This is getting a little boring.
template< typename T >
std::set< T > operator-( const std::set< T > &a,
const std::set< T > &b )
{
std::set< T > out;
std::set_difference( a.begin(), a.end(),
b.begin(), b.end(),
std::inserter( out, out.begin() ) );
return out;
}
And finally the symmetric difference. Surprise!
template< typename T >
std::set< T > operator^( const std::set< T > &a,
const std::set< T > &b )
{
return ( a | b ) - ( a & b );
}
int main() /* demo */
{
std::set a{ 1, 2, 3 };
std::set b{ 1, 3, 5 };
std::set aib{ 1, 3 };
std::set aub{ 1, 2, 3, 5 };
std::set amb{ 2 };
std::set axb{ 2, 5 };
PB161 Programming in C++ 72/114 June 28, 2022
assert( ( a & b ) == aib );
assert( ( a | b ) == aub );
assert( ( a - b ) == amb );
assert( ( a ^ b ) == axb );
assert( ( a & b ) == ( b & a ) );
assert( ( a | b ) == ( b | a ) );
assert( ( a - b ) != ( b - a ) );
assert( ( a ^ b ) == ( b ^ a ) );
}
10.d.5 [call] The final example will deal with the function call operator,
also known as operator(). This will allow us to construct objects
which can be called, just like lambdas. However, there is one thing that
lambdas can’t do very well in C++, and that is provide multiple overloads.
Likewise, standard top-level functions cannot be easily passed
as arguments to other functions, since overload sets are not first-class
in C++: instead, we have to wrap up the overload set in a callable object.
We will see that in a minute.
We will re-use the same construction that we have seen in apply.cpp,
but we will allow different value types to appear in the tree, instead of
just integers. We will again define null as the empty tree:
struct null {};
Even though the struct above is empty, we need to define equality if
we want to use it. Since it will be rather useful in writing tests later,
we will define the (trivial) equality operator here:
bool operator==( null, null ) { return true; }
Like other functions defined on recursive data types, we first need to
define the base case for map, i.e. the case when the subtree is empty:
template< typename fun_t >
auto map( null, const fun_t & )
{
return null();
}
And instead of sum, we will have a generic mapping operator:
template< typename val_t, typename left_t, typename right_t,
typename fun_t >
auto map( const std::tuple< val_t, left_t, right_t > &tuple,
const fun_t &fun )
{
const auto &[ val, left, right ] = tuple;
return std::tuple{ fun( val ),
map( left, fun ), map( right, fun ) };
}
The call operator uses syntax very similar to the indexing operator
which we have seen before, just with parentheses instead of square
brackets. Since () is the name of the operator, the arguments need to
come in another pair of parens. Please keep that in mind!
struct to_string
{
std::string operator()( int i ) const
{
return std::to_string( i );
}
std::string operator()( const std::string &s ) const
{
return s;
}
};
A small thing that we have not seen yet. Normally, if we want to
construct an object, we need to call its constructor, e.g. std::string(
"hello" ). Sometimes, this is quite tedious, like in this example. C++
offers a feature called user-defined literals, where we are allowed to
overload certain operators which then make it possible to create object
instances using literal syntax. We will not get into the details of
creating such user-defined literals, but we will use the one that the
standard library provides for constructing std::string instances. To
use them, we need to use the following declaration first, to get the
literal operators into scope:
using namespace std::literals;
int main() /* demo */
{
After the using namespace above, we can say "hello"s to mean
std::string( "hello" ). Saves us a bit of typing.
std::tuple a{ "hello"s, null(), null() };
std::tuple b{ 7, null(), null() };
std::tuple c{ "x"s, a, b };
std::tuple b_str{ "7"s, null(), null() };
std::tuple c_str{ "x"s, a, b_str };
assert( map( a, to_string() ) == a );
assert( map( b, to_string() ) == b_str );
assert( map( c, to_string() ) == c_str );
}
Part 10.e: Elementary Exercises
10.e.1 [format] In this exercise, we will practice writing functions with
more complex argument deduction. The functions in question will
use std::ostringstream to produce string representation of sets and
vectors.
Use a comma-separated format for std::vector instances, with arbitrary
element type, then do the same for std::set. Vectors should use
square brackets [] and sets should use curly braces {} as delimiters. Assume
the value_type stored in the vector has appropriate std::ostream
operators. The functions should be called format.
10.e.2 [concat] Write a function which takes two sequences, a and
b, and produces a single vector with values from the two sequences
(first all values from a, then all values from b, preserving their order).
Assume each sequence has a nested typedef value_type. The sequences
do not need to be of the same type, but their values must be compatible.
// … concat( … a, … b )
10.e.3 [select] Write a function which returns a vector of variants,
such that the i-th position is taken from input a iff which[ i ] is true and
from input b otherwise. Both a and b must have at least which.size()
elements. Elements beyond this size are ignored. Both a and b are
sequences with a value_type nested typedef.
// … select( … a, … b, const std::vector< bool > &which );
Part 10.p: Preparatory Exercises
10.p.1 [post] The goal of this exercise is simple: take an oriented graph
as the input and produce a list (vector) of vertices in the ‘leftmost’ DFS
post-order. That is, visit the successors of a vertex in order, starting
from leftmost (different exploration order will result in different postorders).
The graph is encoded as a neighbourhood list.
template< typename value_t >
using graph = std::map< value_t, std::vector< value_t > >;
Construct the post-order of g starting from vertex i.
PB161 Programming in C++ 73/114 June 28, 2022
// … dfs_post( … g , … i );
10.p.2 [cons] We will elaborate a little on the topic from icons.cpp, by
making the type of car into a template argument. That way, we will
be able to make a list that has items of different types in it.
Generalize cons from the previous exercise and write a reduce function
that takes an arbitrary cons instance, a function object (e.g. a lambda)
and an initial accumulator value. The function object must be able to
accept the accumulator as its first argument, and an arbitrary value
that appears in the cons list as its second argument.
null, cons, reduce
callable object with overloads, for testing
struct collect
{
using pair = std::pair< int, double >;
pair operator()( pair p, int i ) const
{
p.first += i;
return p;
}
pair operator()( pair p, double d ) const
{
p.second += d;
return p;
}
};
10.p.3 [map] Write keyset, a function which takes an instance of
std::map and returns an std::set with the keys that were present in
the input map.
And intersect, which takes an std::set of keys and an std::map (with
the same key type and arbitrary value type) and produces another
std::map which only retains the key/value pairs for which keys were
present in the input key set.
10.p.4 [collect] The goal of this exercise is to write a set of overloads
that will, together, allow the user to extract values from standard containers,
into a vector. For std::map and std::unordered_map, this means
the value without the key. For other container types, the functions
simply copy the contents into an output vector.
10.p.5 [list] In this exercise, we will define a list class that behaves
like the lists in functional programming: the values and structure will
be immutable, but it’ll be possible to fairly cheaply create new lists by
prepending values to existing lists.
Define a class template list with a singe type parameter T, with the
following interface (all methods are const):
• head returns the value of the current list
• tail returns the remainder of the list as another list instance, without
copying any values
• empty which returns true if the list is empty
• a default constructor which creates an empty list (i.e. the [] constructor
you know from Haskell)
• a 2-parameter constructor which takes the value and the tail of the
list (i.e. the (:) constructor).
Hint: It is preferable to store the values inline in the nodes. You should
also use 2 data types, one for the list itself and another for nodes: this
will make it easier to implement empty lists and in general make the
implementation nicer.
template< typename T >
class list; /* ref: 24 lines */
10.p.6 [tree] In this exercise, we will implement an immutable binary
tree, similar to the list we saw earlier.
Implement class template tree with a single type argument T and the
following interface (all method are const):
• the default constructor creates an empty tree,
• a 3-parameter constructor creates a tree with the value given in
the first argument as root and the next two arguments specify the
left and right subtrees,
• a 1-parameter constructor creates a leaf node which stores the value
given in the argument,
• empty returns true if the tree is empty,
• root returns a reference to the value in the root,
• left returns the left subtree,
• right returns the right subtree.
Hint: two of the constructors can be merged using default arguments.
template< typename T >
class tree;
Part 10.r: Regular Exercises
10.r.1 [icons] In this exercise, your goal will be to define a list-like
structure using templates, and then recursively sum numbers stored
in it. You will need to use both templates and function overloading.
In LISP-like languages, lists are built out of so-called cons cells (cons
being short for constructor). Each cell contains a value and a pointer
to the next cell. The value is traditionally called car and the pointer to
the next cell is called cdr. The cdr may also be null, i.e. an empty list. In
our case, the car will always be of type int. The cdr will be given by a
template parameter, in the expectation that it is another cons instance
or null.
struct null {}; /* empty */
template< typename cdr_t >
struct cons;
Overloads and/or templates of sum go here.
10.r.2 [sorted] Write a function object that will decide, when passed
to foreach, whether the iterated sequence was sorted in ascending
order. The result is obtained by calling was_sorted on the object after
the iteration ends.
It might be useful to know that std::any can hold a value of any
type. Use normal assignment to store a value in an any instance and
std::any_cast to read the value back.
struct check_sorted;
Unlike std::foreach, we take the function by reference, which makes
it possible to inspect its state after iteration ends.
template< typename iter_t, typename fun_t >
void foreach( iter_t b, iter_t e, fun_t &&f )
{
while ( b != e )
f( *b++ );
}
10.r.3 [fsm] Everyone’s favourite: deterministic finite state machines.
We will write a class template that will let us decide whether a generalized
word (a sequence of values of a type equipped with equality)
belongs to a regular language described by a given finite automaton
(finite state machine) or not. The type which represents individual
letters is given to fsm as a type parameter.
The constructor of fsm should accept a single boolean (mark the constructor
explicit), which determines if the state represented by the
instance is accepting or not. A default-constructed fsm should be nonaccepting.
Make the following methods available:
• next which accepts a letter (of type letter_t) and a const reference
to another fsm instance; the method adds a transition to the automa-
PB161 Programming in C++ 74/114 June 28, 2022
ton,
• accept which takes a sequence of letter_t values (the type of the
sequence is not fixed, but it can be iterated using a range for) and returns
true if the automaton accepts the word stored in the sequence;
this method should be marked const.
// … class fsm;
10.r.4 [bimap] Implement bimap, a container with 2 key types (say
left_t and right_t) and the following interface:
• insert( left_t, right_t ) establish a mapping and return true, or
return false if either of the passed keys is already mapped (to the
same or a different value),
• get_left( right_t ): return a pointer to the left key corresponding
to a given right key or nullptr if not present,
• get_right( left_t ): the opposite,
• erase( left_t, right_t ) remove a mapping.
10.r.5 [tinyvec] † Implement tiny_vector, a class which works like a
vector, but instead of allocating memory dynamically, it uses a fixedsize
buffer which is part of the object itself (use e.g. an std::array of
bytes). The number of elements it should be able to accommodate is
given as a template parameter, along with the type of the element.
Provide the following methods:
• insert (take an index and an rvalue reference),
• erase (take an index),
• back and front, with appropriate return types.
In this exercise (unlike in most others), you are allowed to use reinter-
pret_cast.
Throw this if insert is attempted but the element wouldn’t fit into the
buffer.
class insufficient_space {};
Hint: Use uninitialized_* and destroy(_at) functions from the memory
header.
template< typename T, size_t max_size >
class tiny_vector;
void do_test();
Part 11: Iterators
XXX
Demonstrations:
1. queue – an iterable queue
2. split – chop up a string_view into pieces
3. glob – iterate over matches of a pattern in a string
Elementary exercises:
1. iota – an iterable sequence of integers
2. view – iterate a slice of an existing collection
3. skip – iterate every n-th item (a stride) of a collection
Preparatory exercises:
1. seq – generic sequences
2. filter – filtered sequences
3. zip – iterate two sequences in lockstep
4. nibble – a fixed-size nibble array
5. tree – in-order iteration of a tree
6. scan – generalized prefix sum
Regular exercises:
1. map – applying a function to a sequence
2. range – views with a shared backing store
3. permute – iterate all permutations of a sequence
4. critbit – iterate a ‘critbit’ binary trie in order
5. matrix † – iterate a compact rectangular array
6. bits – iterate bits in a word
Part 11.d: Demonstrations
11.d.1 [queue] We will now implement a data structure ‘from scratch’
(i.e. without using std containers) using templates. Again, you may
find it useful to go back to 06/queue.cpp and compare the two imple-
mentations.
Like before, since we are going for a custom, node-based structure,
we will need to first define the class to represent the nodes. Unlike
the previous implementation, however, the node itself needs to be
parametrized by the type of the value it should hold.
template< typename T >
struct queue_node
{
You may have noticed this with the zipper earlier: we do not need to
mention the type parameter when we want to refer to the instance of
queue_node where T is T (though we can if we want to). In other words,
within queue_node, saying queue_node when referring to a type means
the same thing as queue_node< T >.
std::unique_ptr< queue_node > next;
The data attribute will be of type T.
T value;
};
Like the node, the iterator also needs to be parametric.
template< typename T >
struct queue_iterator
{
Here, we have no choice but to explicitly spell out the type parameter
of queue_node, since we are no longer within that class.
queue_node< T > *node;
Constructor names are unaffected by templates.
queue_iterator( queue_node< T > *n ) : node( n ) {}
The pre-increment operator simply shifts the pointer to the next
pointer of the currently active node. This method is unchanged from
the non-generic version.
queue_iterator &operator++()
{
node = node->next.get();
return *this;
}
The implicit ‘current instance of the template’ shortcut works in arguments
too, including in arguments of friend functions, so let’s demonstrate
that:
friend bool operator!=( const queue_iterator &a,
const queue_iterator &b )
{
return a.node != b.node;
}
PB161 Programming in C++ 75/114 June 28, 2022
Finally the dereference operator. Unlike before, we don’t know much
about T, hence we prefer to always return a reference, even in the
const overload.
T &operator*() { return node->value; }
const T &operator*() const { return node->value; }
};
The queue itself will be a template too, of course.
template< typename T >
class queue
{
Like in the iterator, we need to instantiate any template classes that
we use that were defined earlier. That is the only difference compared
to our earlier queue implementation.
std::unique_ptr< queue_node< T > > first;
queue_node< T > *last = nullptr;
public:
In the integer-only version, we passed the argument by value, but like
in the dereference operator above, we will now instead use a const
reference: T might be a big class with an expensive copy operation. We
do not want to do that twice.
void push( const T &v )
{
if ( last ) /* non-empty list */
{
Notice the T in the make_unique call.
last->next = std::make_unique< queue_node< T > >();
last = last->next.get();
}
else /* empty list */
{
first = std::make_unique< queue_node< T > >();
last = first.get();
}
last->value = v;
}
Now we run into a bit of a problem. Since making copies of T is possibly
expensive, we would like to return a reference: but we cannot, since
pop will destroy the node which stores the value. Incidentally, this is
the reason why std::queue::pop is a void function and you need to use
a separate front call to get the value. We will simply return by value
instead, which can be less efficient, but not terribly so. We can reduce
the cost by using std::move on the value, since the node is going to be
destroyed anyway.
T pop()
{
T v = std::move( first->value );
first = std::move( first->next );
Do not forget to update the last pointer in case we popped the last
item.
if ( !first ) last = nullptr;
return v;
}
The emptiness check is simple enough.
bool empty() const { return !last; }
Same as before, but we need to instantiate the queue_iterator template.
queue_iterator< T > begin() { return { first.get() }; }
queue_iterator< T > end() { return { nullptr }; }
Same.
void erase_after( queue_iterator< T > i )
{
assert( i.node->next );
i.node->next = std::move( i.node->next->next );
}
};
int main() /* demo */
{
We start by constructing an (empty) queue and doing some basic operations
on it. We start by inserting and removing a single element.
queue< std::pair< long, long > > q;
assert( q.empty() );
q.push( { 7, 0 } );
assert( !q.empty() );
assert( q.pop() == std::pair( 7l, 0l ) );
assert( q.empty() );
Now that we have emptied the queue again, we add a few more items
and try erasing one and iterating over the rest.
q.push( { 1, 0 } );
q.push( { 2, 0 } );
q.push( { 7, 0 } );
q.push( { 3, 0 } );
We check that erase works as expected.
queue_iterator i = q.begin();
++ i;
assert( *i == std::pair( 2l, 0l ) );
q.erase_after( i );
We can still use instances of queue in range for loops, because they
have begin and end, and the types those methods return (i.e. iterators)
have dereference, inequality and pre-increment. Since our current
instance of queue contains pairs, we can also use structured bindings
in the for loop.
int x = 1;
for ( auto [ v, w ] : q )
{
assert( v == x++ );
assert( w == 0 );
}
That went rather well, let’s just check that the order of removal is the
same as the order of insertion (first in, first out). This is how queues
should behave.
assert( q.pop() == std::pair( 1l, 0l ) );
assert( q.pop() == std::pair( 2l, 0l ) );
assert( q.pop() == std::pair( 3l, 0l ) );
assert( q.empty() );
}
11.d.2 [split] We will forego templates for a bit and implement a fullfeatured
input iterator: the most basic kind of iterator that can be used
to obtain values (as opposed to updating them, as done by an output
iterator).
A common task is to split a string into words, lines or other delimiterseparated
items. This is one of the cases, where the standard library
does not offer any good solutions: hence, we will roll our own. The
class will be called splitter and will take 2 parameters: the string
(string_view to be exact) to be split, and the delimiter (for simplicity
PB161 Programming in C++ 76/114 June 28, 2022
limited to a single character).
The splitter is based on string_view to make the whole affair ‘zerocopy’:
the string data is never copied. The downside is that the input
string (the one being split) must ‘outlive’ the splitter instance.
You might remember the function split from week 9: we will use that
as the ‘workhorse’ of the splitter.
using split_view = std::pair< std::string_view, std::string_view >;
split_view split( std::string_view s, char delim )
{
size_t idx = s.find( delim );
if ( idx == s.npos )
return { s, {} };
else
return { s.substr( 0, idx ), s.substr( idx + 1, s.npos ) };
}
The splitter class itself doesn’t do much: its main role is to create
iterators, via begin and end. To this end, it must of course remember
the input string and the delimiter.
struct splitter
{
using value_type = std::string_view;
std::string_view _str;
char _delim;
Real iterators must provide operator-> – the one that is invoked when
we say iter->foo(). For this particular use-case, this is a little vexing:
operator-> must return either a raw pointer, or an instance of a class
with overloaded operator->. Clearly, that chain must end somewhere
– sooner or later, we must have an address of the item to which the
iterator points.
This is inconvenient, because we want to construct that item ‘on the fly’
– whenever it is needed – and return it from the dereference operator
(unary *) by value, not by reference.
The above two requirements are clearly contradictory: as you surely
know, returning the address of a local variable won’t do. This is where
proxy comes into play: its role is to hold a copy of the item that has
sufficiently long lifetime.
Later, we will return proxy instances by value, hence proxy itself will
be a temporary object. Since temporary objects live until the ‘end of
statement’ (i.e. until the nearest semicolon, give or take), we can return
the address of its own attribute. That address will be good until the
entire statement finishes executing, which is good enough: that means
when we write iter->foo(), the proxy constructed by operator->, and
hence the string_view stored in its attribute, will still exist when foo
gets executed.
struct proxy
{
value_type v;
value_type *operator->() { return &v; }
};
struct iterator
{
There are 5 ‘nested types’ that iterators must provide. The probably
most important is value_type, which is the type of the element that we
get when we dereference the iterator.
using value_type = splitter::value_type;
The iterator_category type describes what kind of iterator this is, so
that generic algorithms can take advantage of the extra guarantees
that some iterators provide. This is a humble input iterator, and hence
gets std::input_iterator_tag as its category.
using iterator_category = std::input_iterator_tag;
The remaining 3 types exist to make writing generic algorithms somewhat
easier. The difference_type is what you would get by subtracting
two iterators – the ‘default’ is ssize_t, so we use that, even though our
iterators cannot be subtracted.
using difference_type = ssize_t;
The last two are ‘decorated’ versions of value_type: a pointer, which is
straightforward (but do remember to take const-ness into account)…
using pointer = value_type *;
… and a reference (same const caveat applies). However, you might find
it surprising that the latter is not actually a reference type in this case.
Why? Because reference is defined as ‘what the dereference operator
returns’, and our operator* returns a value, not a reference. Input
iterators have an exception here: all higher iterator types (forward,
bidirectional and random) must make reference an actual reference
type.
using reference = value_type;
Now, finally, for the implementation. The data members (and the
constructor, and the assignment operator) are all straightforward. The
_str attribute represents the reminder of the string that still needs to
be split, and will be an empty string for the end iterator. Remember
that string_view does not hold any data, so we are not making copies
of the input string.
std::string_view _str;
char _delim;
iterator( std::string_view s, char d )
: _str( s ), _delim( d )
{}
iterator &operator=( const iterator & ) = default;
The pre-increment and post-increment operators are reasonably simple.
As is usual, we implement the latter in terms of the former.
iterator &operator++()
{
_str = split( _str, _delim ).second;
return *this;
}
iterator operator++( int )
{
auto orig = *this;
++*this;
return orig;
}
Dereference would be unremarkable, except for the part where we
return a value instead of a reference (we could use the reference nested
type here to make it clear we are adhering to iterator requirements,
but that would be likely more confusing, considering how reference is
not a reference). Do note the const here.
value_type operator*() const
{
return split( _str, _delim ).first;
}
This is what gets called when we write iter->foo. See proxy above for
a detailed explanation of how and why this works. Also, const again.
proxy operator->() const
{
return { **this };
}
PB161 Programming in C++ 77/114 June 28, 2022
Finally, equality. There is a trap or two that we need to avoid: first and
foremost, string_view comparison operators compare content (i.e. the
actual strings) – this is not what we want, since it could get really slow,
even though it would ‘work’.
The other possible trap is that on many implementations, string literals
with equal content get equal addresses, i.e. the begin of two different
std::string_view( "" ) instances would compare equal, but this is not
guaranteed by the standard. It just happens to work by accident on
many systems.
bool operator==( const iterator &o ) const
{
return _str.empty() && o._str.empty() ||
_str.begin() == o._str.begin();
}
bool operator!=( const iterator &o ) const
{
return !( *this == o );
}
};
auto begin() const { return iterator( _str, _delim ); }
auto end() const { return iterator( {}, _delim ); }
splitter( std::string_view str, char delim )
: _str( str ), _delim( delim )
{}
};
int main() /* demo */
{
auto s = splitter( "quick brown fox", ' ' );
auto e = std::vector{ "quick", "brown", "fox" };
auto iseq = [&]{ return std::equal( s.begin(), s.end(),
e.begin(), e.end() ); };
assert( iseq() );
s = splitter( "", ' ' );
assert( !iseq() );
e.clear();
assert( iseq() );
s = splitter( "hello", ' ' );
e = std::vector{ "hello" };
assert( iseq() );
s = splitter( "hello", 'l' );
e = std::vector{ "he", "", "o" };
assert( iseq() );
}
11.d.3 [glob] TBD
Part 11.e: Elementary Exercises
11.e.1 [iota] Write a class iota, which can be iterated using a range for
to yield a sequence of numbers in the range start, end - 1 passed to
the constructor.
class iota;
11.e.2 [view] Write a class template view which will allow us to bundle
a pair of iterators of an existing sequence and use them as a virtual
sequence in its own right. It should be possible to change the underlying
sequence through the view. The constructor should accept two
iterators, start and end, and iterating the resulting sequence should
include everything in this range (end is excluded, as is customary).
// … class view;
11.e.3 [skip] Write a class template skip which will be like a view, but
allow us to iterate every n-th item (a stride) of a given iterator range,
instead of every item. Make sure that if the stride does not evenly
divide the sequence length, iteration still works correctly.
Hint: please note that this class is significantly more complicated than
view was. You might find decltype( auto ) useful, particularly as the
return type of a function.
Part 11.p: Preparatory Exercises
11.p.1 [seq] In this exercise, the goal will be to implement a class template
which will allow us to iterate over a sequence of number-like
objects.
The seq class should be constructible from 2 number-like objects:
the initial value (included) and the final value (excluded). Use preincrement
(operator ++) and equality (operator ==) to generate the values.
The dereference operator should return the generated objects by
value.
template< typename T >
class seq_iterator; /* ref: 10 lines */
template< typename T >
class seq; /* ref: 9 lines */
A nat implementation for testing purposes.
struct nat
{
int v;
nat( int v ) : v( v ) {}
bool operator==( nat o ) const { return v == o.v; }
nat &operator++() { ++v; return *this; }
};
11.p.2 [filter] Lazy sequences, part two.
Define a class template, filter, which holds two items:
• a reference to an arbitrary container,
• a lambda f (of type a → bool).
The constructor of filter should accept both, in this order. It should
be possible to use instances of filter in range for loops: each element
from the underlying container is first passed to f and if the result is true,
is returned to the user (via the dereference operator), otherwise it is
discarded. You may want to review map.cpp in this unit and filter.cpp
from week
7.
template< typename, typename >
struct filter_iterator; /* ref: 25 lines */
template< typename, typename >
struct filter; /* ref: 11 lines */
11.p.3 [zip] Lazy sequences, part three.
Define a class template, zip, which holds 2 references to arbitrary
containers, possibly of different types.
The constructor of zip should accept both (via const references). It
should be possible to use instances of zip in range for loops: in each
iteration, the zip iterator fetches a single elemnt from each of the two
containers and returns them as a 2-tuple of const references. The
iteration ends when the shorter of the two sequences runs out of
elements.
Hint: to create a tuple of references, use std::tie.
template< typename, typename >
PB161 Programming in C++ 78/114 June 28, 2022
struct zip_iterator; /* ref: 31 lines */
template< typename, typename >
struct zip; /* ref: 11 lines */
11.p.4 [nibble] In this exercise, we will create a fixed-size array of
nibbles (half-bytes), with an indexing operator and with a basic iterator.
You may want to refer back to 05/nibble.cpp for details about operators.
The class template nibble_array should take a single size_t-typed nontype
template argument. It should be possible to index the array and
to iterate it using a range for loop. The storage size should be the least
required number of bytes. Default-constructed nibble_array should
have zeroes in all its entries.
template< size_t N >
class nibble_array;
11.p.5 [tree] Write an iterator class and 2 functions, tree_begin and
tree_end, which given a proper binary tree (by const reference) construct
an iterable range which visits each node of the tree once. The
iteration should proceed in-order, that is, the entire left subtree is visited
before the current node, and the right subtree afterwards.
template< typename value_t >
struct tree
{
std::unique_ptr< tree > left, right;
tree *parent = nullptr;
value_t value;
static auto make_tree( const tree &t, tree *parent )
{
return std::make_unique< tree >( t, parent );
}
tree( const tree &t, tree *parent )
: left( t.left ? make_tree( *t.left, this ) : nullptr ),
right( t.right ? make_tree( *t.right, this ) : nullptr ),
parent( parent ),
value( t.value )
{}
tree( value_t value, const tree &l, const tree &r )
: left( make_tree( l, this ) ),
right( make_tree( r, this ) ),
value( std::move( value ) )
{}
tree( value_t value )
: value( std::move( value ) )
{}
};
Given a tree t, construct the two end-points of the iterator range:
// … tree_begin( … t );
// … tree_end( … t );
11.p.6 [scan] Implement a class template scan, which computes a generalized
prefix sum. This is essentially a fold, but instead of simply
returning the final value, it also returns all the intermediate results. It
should be possible to iterate instances of scan using a range for loop.
Example: a scan of a sequence with elements 1, 2, 3 and 4, using
std::plus, and initial value 0 should yield the sequence 1, 3, 6, 10.
The constructor, which should enable class template argument deduction,
takes 3 arguments:
• a const reference to a container with value_type = T,
• a lambda with the signature S( T, S ), and
• an initial value of type S, by value.
NB. Do not assume that values of either type S or T can be copied.
Values of type S can be default-constructed though.
Part 11.r: Regular Exercises
11.r.1 [map] Lazy sequences, part one.
Define a class template, map, which holds two items:
• a reference to an arbitrary container,
• a lambda f (of type a → b).
The constructor of map should accept both (via const references), in this
order. It should be possible to use instances of map in range for loops:
each element from the underlying container is first passed to f and
the result of that is returned to the user (via the dereference operator).
Hint: the type of the iterator that const versions of begin and end return
is available in standard containers as a nested type, like this: std::vector<
int >::const_iterator.
11.r.2 [range] We have mostly ignored the question of ownership
when we worked with on-the-fly map and filter implementations in
previous exercises: it was up to the user to ensure that the underlying
container outlives the range object. However, we may sometimes
want to be able to return such mapped ranges from functions which
construct the underlying data, and this does not work in our previous
model. Let’s try a different approach then.
Define a class template range which takes a container as a template
argument. The class should offer the following interface (all methods
are const):
• construction from a container, with argument template deduction
(we will make a copy of the container: in real world, we would be
able to avoid doing that),
• iteration interface: begin and end which return suitable iterators
(usable in range for at minimum),
• take and drop which construct a new range object that shares the
backing data with the current one, but offer a reduced view of it
(take reduces the view to first N elements, while drop removes the
first N elements from the view),
• an element-wise equality comparison operator (we want this to
work with ranges backed by different containers, so you will need
to implement this operator as a template).
template< typename container_t >
class range;
11.r.3 [permute] Implement class permutations, with a constructor
which accepts an std::vector of int and which represents a sequence
of all distinct permutations of the input vector. Iterating an instance
of permutations should yield values which can be both iterated and
indexed, yielding, in turn, integers. The permutations object itself does
not need to be indexable. For example:
std::vector vec{ 1, 3, 2 };
for ( auto p : permutations( vec ) )
for ( int v : p )
std::cerr << v << " ";
The first permutation should be sorted in ascending order. The sequence
of permutations as a whole should be sorted in lexicographic
order (as a consequence of this, the last permutation should be sorted
in descending order). The output of the above program, therefore,
should be: 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1.
11.r.4 [matrix] † Implement a class which stores a compact N×M array
of scalars (given by its template parameter). Assume that the scalars
can be copied and default-constructed, but avoid constructing unnecessary
copies. The data is passed into the constructor as a single std::initializer_list<
scalar_t > with N×M entries, in row order, starting in
the top left corner.
PB161 Programming in C++ 79/114 June 28, 2022
The class should have 2 methods: cols and rows. The result of each
should be iterable, and each element yielded should be iterable again,
yielding the corresponding scalars.
template< typename scalar_t, size_t ncols, size_t nrows >
class matrix;
void do_test();
11.r.5 [bits] Implement a class template bits that, when iterated, yields
individual bits of the number passed into its constructor, as boolean
values.
template< typename number_t >
class bits;
Part 12: Review
Since this is a review chapter with no new material in it, there are
no demonstrations. You can refer to previous chapters and lectures if
you encounter concepts that you do not know, or which you need to
refresh.
Elementary exercises:
1. digraph – count digraph frequency
2. spelling – a very simple spell checker
3. ternary – ternary logic
Preparatory exercises:
1. chords – naming minor and major 5 & dominant 7 chords
2. grammar – generate words from regular grammars
3. linear – simple linear equations with a parser
4. poly – searching for roots of polynomials
5. queens – checking a solution of the 8 queens puzzle
6. map – more mapping of sequences
Regular exercises:
1. trie – binary tries with wildcards
2. cooking – storing recipes
3. cards – parsing and comparing playing cards
4. minilisp – a small LISP-like language parser
5. language – detect language of a text fragment
6. union – the union-set data structure
Part 12.e: Elementary Exercises
12.e.1 [digraph] We will write a simple function, digraph_freq, which
accepts a string and computes the frequency of all (alphabetic) digraphs.
The exact signature is up to you, in particular the return type. The only
requirement is that the returned value can be indexed using strings
and this returns the count (or 0 if the input string is not a correct
digraph). This must also work on const instances of the return value.
For examples see main.
Define digraph_freq here, along with any helper functions or classes.
12.e.2 [spelling] The file /usr/share/dict/words contains one English
word per line. Write a class, spell, the constructor of which takes the
path to a file of this type (one word per line) and with a single method,
check, which takes an std::string which contains a single word and
returns true if the word is in the provided list.
class spell;
12.e.3 [ternary] Ternary (or 3-valued) logic uses 3 different truth values:
true, false and unknown (maybe).
Define a suitable type tristate and 3 constants yes, no and maybe (to
avoid conflicts with built-in boolean constants), along with the standard
logical operators and equality.
Part 12.p: Preparatory Exercises
12.p.1 [chords] We will write a simple program to compute and format
chords (as in music). Partition the code as you see fit.
The entire western musical scale has 12 notes in it, one semitone (100
cents) apart. Chords are built up from minor (300 cents) and major
(400 cents) thirds. We will only deal with chords in the root position,
i.e. where the root note is in the bass and we’ll use the German names:
• c, d, e, f, g, a and h are the ‘base’ notes
• cis, dis, eis = f, fis, gis, ais, his = c are sharps,
• ces = h, des, es, fes = e, ges, as and b are flats.
Base notes are 200 cents apart, except the e/f and h/c pairs, which are
100 cents apart. A flat subtracts, and a sharp adds, 100 cents to the
base note. The simplified rules for using note names in chords are as
follows:
• key is E, G, A, H, D or any note with a sharp → use sharps,
• key is F or a note with a flat → use flats,
• flats and sharps are not mixed in basic chords,
• ignore double flats and double sharps
• instead of eis, his, ces and fes, use f, c, h and e.
A (pure) fifth is 700 cents and a minor 7th is 1000 cents. Intervals (in
cents) are composed using addition, mod 1200. By convention, ‘c’ is
0. For instance, if the root is ‘g’, that is 700 cents, adding a pure fifth
yields 1400 mod 1200 = 200 = ‘d’. Notes ‘g’ and ‘d’ are a fifth apart.
The major fifth chord starts at the key note (tonic) + a major third +
minor third, e.g. ‘c’ → ‘c e g’ or ‘e’ → ‘e gis h’.
std::string major_5( std::string key );
The root of a minor fifth chord is a sixth above the key note and adds
a minor third + a major third, e.g. ‘c‘ → ‘a c e’ or ‘e’ → ‘cis e gis’. Alternatively,
you could think of it as a minor third below the key note, the
key note itself, and a major third above.
std::string minor_5( std::string key );
The root of a dominant 7th chord is a fifth above the key note (tonic):
for key ‘c’, the root of the dominant is ‘g’. On top of the root, add a major
third, a minor third, and another minor third. E.g. ‘f’ → ‘c e g b’
std::string dominant_7( std::string key );
ref: 42 lines in 4 helper functions, major_5, minor_5 & dominant_7
are each 1 line
12.p.2 [grammar] A regular grammar has rules of the form A → xB or
A → x where A and B are non-terminals and x is a terminal.
Implement class grammar which is default-constructible and has 2 meth-
ods:
• add_rule, which takes 2 or 3 arguments: a single char for the lefthand
non-terminal (a capital alphabetic letter), a terminal and optionally
another non-terminal,
• generate, a const method which takes 2 arguments: the starting
non-terminal and an integer which gives the maximum length of a
word, and returns an std::vector of std::string with all the words
the grammar can generate (within the given size bound), sorted
lexicographically.
class grammar;
PB161 Programming in C++ 80/114 June 28, 2022
12.p.3 [linear] Remember the linear equation solver from 06/p6_linear.cpp?
Let’s do that again, but this time with a simple parser instead
of operator overloading.
Write a function solve which takes a string as its input, and returns
an std::pair of floating point numbers. The input contains 2 linear
equations, one per line, with 2 single-letter alphabetic variables and
integer coefficients. The result should be ordered alphabetically (e.g. x,
y).
std::pair< double, double > solve( const std::string &eq );
ref: solve 26 lines, helper class 19 lines
12.p.4 [poly] In this exercise, we will find at least one (real) root of an
odd-degree polynomial (this is guaranteed to exist, and is comparatively
easy to find using the intermediate value theorem and binary search).
Write function find_root which takes 2 arguments:
• a vector of coefficients (each represented as a double), sorted from
the highest-degree to the lowest, e.g. x3
− 3x + 2 is represented as
the vector { 1, 0, -3, 2 },
• an std::pair with a lower and an upper bound on the value of the
root.
The function should return a root x, that is, a number for which the
polynomial evaluates to zero, e.g. x = −2 for the above example.
The pre-condition is that the bounds evaluate to numbers with opposite
signs (and hence the interval must contain at least one root). There
might be multiple roots in the interval, though: it does not matter
which one the function finds. The returned double should be within
`1e-5` of the actual value of the root.
using bounds = std::pair< double, double >;
using poly = std::vector< double >;
double find_root( const poly &, bounds ); /* ref: 28 lines */
12.p.5 [queens] Write a function that checks whether a given configuration
of 8 queens on a chessboard is such that no two queens endanger
each other.
The first number is the column numbered from left, a = 1, b = 2, ...;
second is the row (likewise indexed from 1, starting at bottom): { 1, 1 }
is the bottom left corner.
using position = std::pair< int, int >;
using queens = std::vector< position >;
Return true if all queens are safe.
bool check( const queens &q ); /* ref: 43 lines */
12.p.6 [map] We will revisit one of the sequence-related constructs
from earlier, that of on-the-fly (on demand) transformation (mapping)
of elements using a given function. In particular, we will look at composing
maps.
In this exercise, you should implement a map view like the one we
did in 11/r1_map, with one improvement: it should also work with
functions which return references. The easiest way to do that is by
creating a type alias using decltype and use that as the return type of
the dereference operator. (Alternatively, look up decltype( auto ) in
cppreference, though that wouldn’t work if you wanted to use the type
as a component of another type.)
Part 12.r: Regular Exercises
12.r.1 [trie] We will implement a binary trie (see 07/p2_bittrie.cpp
for more details about the data structure) with a twist.
The user will manage the nodes explicitly, for two reasons: doing it
automatically is a fair amount of work, and we want to be able to share
subtrees. In particular, our present trie implementation will be able to
encode 0 and 1 bits in a key, but also a ?: a bit which will not affect the
outcome. The easiest way to achieve this is by pointing both the left
and the right pointer of a tree to the same child node. To make things
even more interesting, each leaf node should be able to reconstruct its
own key, with question marks always taken to be ones. The interface:
• root returns a suitable pointer to the root node,
• add takes a suitable node pointer (the parent node), and the bit to
append (a bool),
• add_amb takes a node and appends a question mark to it,
• find takes an std::vector of bool and returns a shared pointer to
the corresponding node (or a nullptr if not found).
The default-constructed trie should be empty. Both add and add_amb
should return a (shared) pointer to the new node. The nodes should
provide the method key which returns an std::vector of bool. The
nodes must not store the entire key.
class trie_node; /* ref: 26 lines */
class trie; /* ref: 30 lines */
12.r.2 [cooking] In this exercise, we will implement a simple model of
cooking, with recipes and a pantry. Try to think about code duplication
and whether you can reduce it and what is the cost of reduction in
duplication.
The class pantry will keep a list of available ingredients and their quantity.
It should be default-constructible and offer a method add, which
takes a string (the name of the ingredient) and an integer (the quantity).
A const method count should take a string (name of the ingredient) and
return the quantity available (possibly 0).
class pantry;
We will use another class to represent recipes (in our simplified world, a
list of ingredients and quantities required to cook a meal). Like pantry, it
should be default-constructible and offer a method add, which accepts
2 or 3 arguments: name, the required quantity and, if supplied, an
optional quantity of the ingredient that will be used if available (in
addition to the required amount) but is not required to cook the meal.
class recipe;
Finally, implement function cook with 3 arguments: a mutable reference
to the pantry which will be used to obtain the ingredients, a const
reference to the recipe to cook and an int, the number of portions to
prepare. The function then returns true if everything went okay (and
of course deducts the ingredients used up from the pantry) or false if
some ingredient was missing or there wasn’t enough of it, in which
case the pantry content remains unchanged.
bool cook( pantry &, const recipe &, int qty );
12.r.3 [cards] In this exercise, we will look back at input/output
streams and formatting operators.
Implement class card which represents one card from the standard
52-card deck, along with operators for input and output. The format is
two letters, first the rank and then the suit. The rank 10 is represented
as T. Use S, H, C and D to represent suits. Do not forget to handle errors.
class card;
PB161 Programming in C++ 81/114 June 28, 2022
Part T.3: Tasks with Templates and Iterators
The programming tasks for this block are as follows:
1. tree.* – iterating trees in post-order,
2. bplus.* – a class template implementing B+ trees,
3. linalg.* – complex and real linear algebra,
4. lisp.* – a simple interpreter for a LISP-like language.
All tasks in this block make some use of templates, which are covered
in chapters 9 and 10, and of course they also rely on knowledge from
previous blocks. Since the first task is about writing iterators, you will
also need to understand the material from chapter 11 to complete it
(though you should be able to make considerable progress with what
you know from chapter 5).
Part T.3.1: [bplus]
The goal of this task is to implement B+ search tree, with insertion and
lookup of keys. Assume that both keys and values can be copied and
that keys can be compared using < and ==.
The max_fanout specifies the ‘branching factor’ b of the tree: the maximum
number of children a node can have. Each node then stores
at most b − 1 keys. As is usual with B trees, the minimum number of
children for an internal node, with the exception of the root, is ⌈b/2⌉
(the upper integral part of b/2).
Each node must be stored in a single contiguous chunk of memory.
That is, at most one memory allocation can be retained across an insert
call (or put differently, all but at most one memory chunk allocated
during insert must be freed before insert returns).
template< typename key_t, typename value_t, int max_fanout >
struct bplus
{
Insert an element, maintaining the invariants of the B+ tree. Must run
in worst-case logarithmic time. Return true if the tree was changed.
bool insert( const key_t &, const value_t & );
Look up elements. The at method should throw std::out_of_range if
the key is not present in the tree. The indexing operator should insert
a default-constructed value if the key is absent, and return a reference
to this value.
bool contains( const key_t & ) const;
value_t &at( const key_t & );
const value_t &at( const key_t & ) const;
value_t &operator[]( const key_t & );
Look up an element and return the path that leads to it in the tree, i.e.
the index of the child node selected during lookup at each level. Return
an empty path if the key is not present. The fetch operation then takes
a path returned by path and fetches the corresponding value from the
tree. Please note that the paths must reflect the layout of a correct B+
tree.
using path_t = std::vector< int >;
path_t path( const key_t & ) const;
const value_t &fetch( const path_t &path ) const;
};
Part T.3.2: [linalg]
In this task, you will implement a few bits of basic linear algebra on
top of an arbitrary scalar field, given as a template parameter. Your
solution will be tested with the complex and real classes from task set
2 (which you will submit along with this solution, see below) and also
using a reference implementation of those classes.
Implement these 2 data types: vector and matrix (please try to avoid
confusing vector with std::vector). In addition to methods prescribed
below, implement the following operators:
• vector addition and subtraction (operators + and -),
• multiplication of a vector by a scalar (from both sides, *),
• dot product of two vectors (operator *),
• matrix addition (operator +),
• multiplication of a vector by a matrix (again *, both sides),
• multiplication of compatible matrices (again *),
• multiplication of matrix by a scalar (* once more),
• equality on both vectors and matrices,
• indexing of vectors to get or change their entries,
• indexing of matrices to get or change their rows.
Note: you need to submit a working version of the ‘complex’ task from
the task set 2 along with this one, including the solution of ‘natural’ if
applicable (though ‘natural’ is not directly required, so only include it
if your solution of task ‘complex’ needs it). Add a copy of the relevant
files to this directory before you submit.
Only the exact arithmetic part of ‘complex’ is required: the approximation
part (abs, arg, exp, log1p) can be left out. You should also add this
(explicit) constructor if you don’t have one: complex( int v ).
// extra files: complex.hpp complex.cpp natural.hpp natural.cpp
#include "complex.hpp" /* required! */
template< typename scalar_ >
struct vector
{
using scalar = scalar_;
explicit vector( int dimension ); /* construct a zero vector */
explicit vector( const std::vector< scalar > & );
int dim() const; /* return the dimension */
};
template< typename scalar_ >
struct matrix
{
using scalar = scalar_;
using vector = ::vector< scalar >;
matrix( int rows, int columns ); /* construct a zero matrix */
explicit matrix( const std::vector< vector > &rows );
The following two methods give the user direct access to the values
stored in the matrix (through column and row vectors). The n is a
0-based index, starting from top (row) or left (column). You may return
const references if appropriate.
vector row( int n ) const;
vector col( int n ) const;
int cols() const;
int rows() const;
Compute basic properties of matrices.
int rank() const;
scalar det() const; /* determinant */
matrix inv() const; /* inverse matrix */
matrix transpose() const; /* transpose matrix */
Performs in-place Gaussian elimination: after the call, the matrix
should be in a reduced row echelon form.
void gauss();
PB161 Programming in C++ 82/114 June 28, 2022
};
Note: the behaviour is undefined if the vector instances passed to a matrix
constructor are not all of the same dimension and when det or inv
are called on a non-square matrix or inv on a singular matrix. Likewise,
operations on dimensionally mismatched arguments are undefined.
All dimensions must be positive.
Part T.3.3: [lisp]
In this task, you will implement a simple programming language interpreter:
the syntax and semantics will be based on LISP. For simplicity,
the only data types will be numbers, symbols and cons cells.
Accept a string that corresponds to the number non-terminal as defined
below. Store the integer part of the input in value and return the
number of characters processed (including the discarded decimal part).
If the input is invalid, return 0.
int from_string( std::string_view s, int &value );
The interpreter itself. The parse and eval methods may be called any
number of times on the same instance, in any order, and must not
interfere with each other.
template< typename number_t_ >
struct lisp
{
struct error_t {}; /* indicates parse or evaluation error */
struct nil_t {}; /* empty list */
struct cons_t; /* list cell */
struct lambda_t; /* lexical closure */
using number_t = number_t_;
using symbol_t = std::string;
using value_t = std::variant< number_t, symbol_t, error_t,
cons_t, nil_t, lambda_t >;
Cons (list) cells are the basic building block of LISP programs. A list
is built by putting values in car’s and the successive tails of the list in
cdr’s. The last cdr of a proper list is always nil_t.
struct cons_t
{
std::shared_ptr< value_t > car, cdr;
};
Syntax:
expr = { space }, ( atom | list ), { space } ;
list = '(', expr, { space, expr }, ')' ;
space = ' ' | ? newline ? ;
atom = symbol | number ;
number = [ sign ], digits, [ '.', digits ] ;
symbol = s_init, { s_cont } | sign ;
digit = '0' | '1' | '2' | '3' | '4' |
'5' | '6' | '7' | '8' | '9' ;
sign = '+' | '-' ;
digits = digit, { digit } ;
s_init = s_char | s_symb ;
s_char = ? alphabetic character ? ;
s_symb = '!' | '$' | '%' | '&' | '*' | '/' | ':' | '<' |
'=' | '>' | '?' | '_' | '~' ;
s_cont = s_init | digit | s_spec ;
s_spec = '+' | '-' | '.' | '@' | '#' ;
If the input string does not conform to the above grammar, return a
value of type error_t. Otherwise, the result is one of number_t, symbol_t,
cons_t or nil_t. A list non-terminal is always parsed as a proper list
or a nil_t.
Assume that if you have number_t n, it is possible to call from_string(
"…", n ) with the above semantics (possibly extended to also handle
the decimal part).
value_t parse( std::string_view expr );
Semantics:
• numbers, nils and lambdas evaluate to themselves,
• symbols evaluate to:
∘ their bound value in the current lexical environment,
∘ error_t if they are unbound,
• lists are evaluated in 3 modes:
∘ () to a nil_t,
∘ as the if, let or lambda special form,
∘ as a closure invocation (symbol arg₁ … argₙ).
Special forms:
• (if cond expr₁ expr₂):
∘ evaluate to expr₁ if cond evaluates to non-zero,
∘ evaluate to expr₂ if cond evaluates to zero,
∘ evaluate to error otherwise,
• (let (name value) expr): evaluate to expr, in a lexical environment
in which name is bound to value recursively (i.e. if value is a lambda,
it may call itself using name),
• (lambda list expr) evaluates to lambda_t (an anonymous closure)
with names of formal arguments given by list.
Closure invocation:
• the symbol in the car position of the list must evaluate to a lambda_t
(the result is error_t otherwise),
• the entire list then evaluates the body of the lambda in the lexical
environment in which the closure was defined,
• extended by binding each formal argument to the corresponding
argₙ, evaluated in the current lexical environment;
• if the number of actual arguments does not match the number of
formal arguments, the entire list evaluates to error.
The top-level lexical environment is empty with the exception of following
builtin functions:
• +, -, *, / which each accepts exactly 2 operands of type number_t and
evaluates to the obvious thing,
• car and cdr which expect exactly one value of type cons_t and evaluate
to its car or cdr part,
• cons which accepts exactly 2 arguments and constructs a list cell
out of them,
• list which accepts arbitrary arguments and returns a cons list of
all of them.
Anything not covered above evaluates to error_t.
value_t eval( value_t expr );
};
Part T.3.4: [tree]
In this task, you will write a simple tree iterator, i.e. an iterator that
can be used to visit all nodes of a tree, in post-order.
First, implement a tree class, with the given interface. This will be the
interface that tree_iterator will use (of course, you can add methods
and attributes to tree as you see fit, but tree_iterator must not use
them).
The tree is made of nodes, where each node can have an arbitrary
number of children and a single value.
template< typename value_t_ >
struct tree
PB161 Programming in C++ 83/114 June 28, 2022
{
using value_t = value_t_;
Substitute for any type you like, but make sure it can be copied, assigned
and compared for equality; again, tree_iterator must not rely
on the details (it can assign and copy values of type node_ref though).
struct node_ref;
These functions provide access to the tree and the values stored in
nodes.
bool empty() const;
node_ref root() const;
node_ref child_at( node_ref, int ) const;
int child_count( node_ref ) const;
const value_t &value( node_ref ) const;
value_t &value( node_ref );
Finally, methods for constructing and updating the tree follow. A tree
iterator must not use them. The child added last has the highest index.
node_ref make_root( const value_t &value );
node_ref add_child( node_ref parent, const value_t &value );
Remove the entire subtree rooted at node.
void erase_subtree( node_ref node );
};
Iterate a given tree in post-order; tree_iterator must be (at least) a
forward iterator. Adding nodes to the tree must not invalidate any
iterators. Removal of a node invalidates the iterators pointing at that
node or at any of its right siblings. Dereferencing the iterator yields
the value of the node being pointed at.
The tree given may or may not be an instance of the above class template
tree, but it will have a node_ref nested type and the access methods
(empty, root, child_at, child_count and value). The value method
might return a reference (like in your implementation above) or a value,
and the iterator must preserve the return type of value when derefer-
enced.
Note: You don’t have to keep the exact form of the following declarations,
but if you decide to replace them, you must make sure that the
new declarations are equivalent in this sense:
• it must be possible to declare values using tree_iterator and
const_tree_iterator template instances as their type,
• it is permissible to call tree_begin and tree_end on both const and
mutable references to the respective tree type and the result type
must match the below declarations.
template< typename tree > struct tree_iterator;
template< typename tree > struct const_tree_iterator;
template< typename tree >
tree_iterator< tree > tree_begin( tree & );
template< typename tree >
tree_iterator< tree > tree_end( tree & );
template< typename tree >
const_tree_iterator< tree > tree_begin( const tree & );
template< typename tree >
const_tree_iterator< tree > tree_end( const tree & );
Part P: Practice Exams
This directory contains 2 practice exams, which you can submit freely.
When you do this for real, you will have 3.5 hours to read the spec,
implement it and submit the solution. Since the tasks are expected to
take you about 2 hours or less, the submission deadline will be strict
and will not be extended.
The practice exam can be submitted at any time, and will be evaluated
immediately after submission. Unlike the real exam, it will be evaluated
every time you submit (a real exam will only be evaluated once,
using the last submission before the deadline).
To submit a practice exam, use one of:
$ pb161 submit pex_a
$ pb161 submit pex_b
Part P.1: Exam A
P.1.1 [xa1_tree] Given a non-empty tree, compute some of its properties
(listed below). Nodes are numbered, with root being node number
1 (do not assume anything else about node numbering). A branch is
a path from the root to a leaf. Each edge is assigned a non-negative
length. The length of a branch is the sum of lengths of all its edges.
using node = int;
using length = int;
using edge = std::pair< length, node >;
using tree = std::multimap< node, edge >;
Ensure that the input really is a tree, i.e. that each node is reachable
by exactly 1 path from the root. All other functions can assume that
is_tree holds for their input.
Hint: in a tree, the number of edges is the number of nodes - 1. Beware
though, the converse does not hold.
bool is_tree( const tree & );
Compute the length of the longest branch.
int longest_branch( const tree & );
Compute the length of the shortest branch.
int shortest_branch( const tree & );
Compute the average length among all branches.
double average_branch( const tree & );
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
P.1.2 [xa2_rpn] Implement function rpn which takes a single
std::string as an argument. The string contains single-digit constants,
operators + (addition), d (distance, i.e. absolute value of difference), *
(multiplication) and s (sum of the entire stack), separated by exactly
single space. If the string does not conform to this description, throw
parse_error. If there are insufficient operands on the stack, throw
stack_empty. In all other cases, return an integer which is the topmost
value on the stack after the computation has finished.
Examples:
"3 2 1 s" → 6
"3 2 1 +" → 3
"3 x 1 +" → parse_error
"31 1 +" → parse_error
"1 +" → stack_empty
"s" → 0
PB161 Programming in C++ 84/114 June 28, 2022
"" → parse_error
" 1" → parse_error
"1 2" → parse_error
Notes:
• RPN operates on a stack of numbers: constants push themselves
onto the stack, operators pop their operands and push the result,
• the initial stack is empty,
• an empty input string is a parse error.
#include <cassert>
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
P.1.3 [xa3_hamilton] Implement function hamilton which takes a single
non-empty directed graph and returns true iff the graph contains a
Hamiltonian cycle, that is, a cycle that visits each vertex exactly once.
It is okay to use a brute-force search. The input graph is given as an
std::map from vertices (integers) to a list of edges:
using edges = std::vector< int >;
using graph = std::map< int, edges >;
The set of vertices is exactly the set of keys in the above map. The
graph is ill-formed if a successor of a vertex does not appear as a key
in the map.
bool hamilton( const graph & );
Here are a few hints:
• if there is a Hamiltonian path in the graph, it visits each vertex: it
does not matter from which vertex you start your search,
• it is okay to use recursion (and it is in fact a good idea): a path which
does not revisit any vertices can be completed to a Hamiltonian
cycle iff at least one of the outgoing edges of the last vertex on the
path either a) completes a Hamiltonian cycle, or b) extends the path
to a new path which does not revisit any vertices and also can be
completed to a Hamiltonian cycle.
#include <cassert>
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
P.1.4 [xa4_shuffle] Implement class shuffle_vec, which stores a sequence
of 32-bit words (like an std::vector of uint32_t), but which
provides access to half-words which alternate between all the odd and
all the even bits in each word. In other words, iterating a sequence of
3 half-words will yield these uint16_t values:
1. even bits of the first word,
2. odd bits of the first word,
3. even bits of the second word.
Same holds for indexed access. New half-words are added to the end
of the sequence using a push_back method.
In addition to half-word access (which uses the standard begin, end and
the indexing operator), the container should also provide read-only
full-word access to the data, using methods raw_begin and raw_end. If
the sequence contains an odd number of half-words, the odd bits of
the last full word should be all set to 0.
The least-significant bit is even, i.e. the bit pattern of each byte is
10101010, where 1 is odd and 0 is even. The half-words are constructed
as follows:
• if full word is abcdefgh ijklmnop qrstuwvx αβγδεζηθ
• the even half-word is bdfhjlnp rtwxβδζθ and,
• the odd half-word is acegikmo qsuvαγεη.
#include <vector>
#include <cstdint>
#include <cassert>
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
Part P.1: Exam B
P.1.1 [xb1_graph] You are given a non-empty undirected graph (represented
as an adjacency list, where for each edge A → B, the edge B →
A is also present) and a map, which assigns a weight to each vertex.
A connected component of an undirected graph is a maximal subgraph
where each vertex is reachable from every other vertex. The weight
of a component is the sum of weights of all its vertices. Connected
components are pairwise disjoint.
using graph = std::map< int, std::vector< int > >;
Assigns a weight to each vertex. You can assume that each vertex is
present in the map.
using weights = std::map< int, int >;
Compute the weight of the lightest component in a given graph with
a given weight mapping (where lightest = smallest total weight).
int lightest_component( const graph &g, const weights &w );
Like above, but take the heaviest component.
int heaviest_component( const graph &g, const weights &w );
Compute the average weight of a component in a given graph with a
given weight mapping.
double average_component( const graph &g, const weights &w );
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
P.1.2 [xb2_parse] Implement a parser for a simple language, which has
atoms (single alphabetic character) and lists, written using parentheses
around space-delimited elements (which can be either atoms or lists).
A few examples of valid inputs:
• x
• (x)
• (x y)
• (x (x y))
And so on and so forth. Write a single function parse which accepts
an std::string, with the following properties:
• the function throws an exception iff the input is ill-formed
• the return value is an object specified below
The object returned by parse should provide the following interface
(all methods are const):
• is_list which returns a boolean,
• items which returns an object which can be iterated (UB if is_list
is false),
• name which returns a char (UB if is_list is true).
PB161 Programming in C++ 85/114 June 28, 2022
Dereferencing an iterator which belongs to the object returned by
items should yield another object with the interface above.
The formal grammar, in EBNF:
item = atom | list;
list = '(', items, ')' | '()' ;
items = { item, ' ' }, item ;
atom = ? character x iff std::isalpha( x ) ? ;
#include <cassert>
#include <string>
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
P.1.3 [xb3_colours] Write a function to compute the smallest possible
number of colours that can colour a given graph. A correct colouring
is such that no edge connects vertices with the same colour. The graph
is given as a set of edges. Edges are represented as pairs, and if (u, v)
is a part of the graph, so is (v, u).
using graph = std::set< std::pair< int, int > >;
int colours( const graph &g );
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
P.1.4 [xb4_packed] Write a bit-packed container, oct_vector, that will
hold individually addressable octal digits (3-bit numbers) with a vectorlike
interface.
For a capacity c = 21w (where c is the number of octal digits), oct_vector
must not use more than 8w (that is 8c/21) bytes of storage (not counting
constant overhead). When calling reserve, the total capacity may be
rounded to the nearest higher multiple of 21 (i.e. to a capacity such
that w is an integer).
To store the data, use an std::vector, and make this vector available (as
a const reference) via data(). Make it possible to construct an oct_vector
from such a data vector and the size of the original oct_vector from
which the data came. The element type of the vector is not important.
Minimal interface: indexing (with assignment), push_back, reserve, capacity,
pop_back. Iterators (begin, end) which can be used in a range for
and with std::distance (a subset of the interface of an input iterator
will do, with the iterator typedefs, dereference, pre-increment and
(in)equality).
struct oct_vector;
What follows are basic test cases for your convenience. You can add
additional test cases into main(): they will be not executed during evaluation,
so it is okay to submit with broken main. However, make sure
to not alter the prototype. Write all your code before main.
Part S: Exercise Solutions
Part S.1: Week 1
S.1.1 [01.e1_predicates]
#define UNIT e1_predicates
#include "test_main.cpp"
bool all_odd( const std::vector< int > &v )
{
for ( int x : v )
if ( x % 2 != 1 )
return false;
return true;
}
bool any_odd( const std::vector< int > &v )
{
for ( int x : v )
if ( x % 2 == 1 )
return true;
return false;
}
bool count_divisible( const std::vector< int > &v, int k, int n )
{
for ( int x : v )
if ( x % k == 0 )
n -= 1;
return n <= 0;
}
S.1.2 [01.e2_palindrome]
#define UNIT e2_palindrome
#include "test_main.cpp"
bool is_palindrome( const std::string &s )
{
for ( int i = 0; i < int( s.size() ); ++i )
if ( s[ i ] != s[ s.size() - i - 1 ] )
return false;
return true;
}
S.1.3 [01.e3_pascal]
#define UNIT e3_pascal
#include "test_main.cpp"
std::vector< int > pascal( int n )
{
n --;
std::vector< int > p;
p.push_back( 1 ); /* n over 0 */
for ( int k = 1; k <= n; ++ k ) /* n over 1 … n */
p.push_back( p.back() * ( n - k + 1 ) / k );
return p;
}
S.1.4 [01.r1_wrap]
#define UNIT r1_wrap
#include "test_main.cpp"
std::string fill( const std::string &in, int columns )
{
std::string out;
int col = 0;
for ( char c : in )
if ( std::isblank( c ) && col >= columns )
out += '\n', col = 0;
else if ( c == '\n' )
out += "\n\n", col = 0;
else
out += c, ++ col;
PB161 Programming in C++ 86/114 June 28, 2022
return out;
}
S.1.5 [01.r2_digits]
#define UNIT r2_digits
#include "test_main.cpp"
std::vector< int > digits( int n, int base )
{
assert( n >= 0 );
std::vector< int > ds;
while ( n > 0 )
{
ds.push_back( n % base );
n /= base;
}
for ( int i = 0; i < int( ds.size() / 2 ); ++ i )
std::swap( ds[ i ], ds[ ds.size() - i - 1 ] );
return ds;
}
S.1.6 [01.r3_sieve]
#define UNIT r3_sieve
#include <vector>
int sieve( int bound )
{
std::vector< bool > s;
s.resize( bound + 1, true );
for ( int i = 2; i <= bound; ++i )
if ( s[ i ] )
for ( int j = i + i; j <= bound; j += i )
s[ j ] = false;
for ( int i = bound; i > 0; --i )
if ( s[ i ] )
return i;
return 0;
}
#include "test_main.cpp"
S.1.7 [01.r4_bsearch]
#define UNIT r4_bsearch
#include <vector>
using intvec = std::vector< int >;
intvec::iterator bsearch( intvec &vec, int val )
{
auto b = vec.begin(), e = vec.end();
while ( b < e ) /* the search interval is not empty */
{
auto mid = b + ( e - b ) / 2;
if ( val < *mid ) e = mid; /* must be in [b, mid) */
if ( val > *mid ) b = mid + 1; /* must be in (mid, e) */
if ( val == *mid ) return mid; /* we found it */
}
return vec.end();
}
#include "test_main.cpp"
S.1.8 [01.r5_qsort]
#define UNIT r5_qsort
#include <vector>
#include <cassert>
int partition( std::vector< int > &vec, int low, int high, int pivot
)
{
while ( vec[ low ] < pivot ) /* the pivot must be in there */
++ low;
int p_index = low;
shuffle anything < pivot to the front while remembering where (in the
second half) we stashed the pivot itself
for ( int i = low + 1; i < high; ++i )
{
if ( vec[ i ] < pivot )
std::swap( vec[ low++ ], vec[ i ] );
if ( vec[ i ] == pivot )
p_index = i;
}
put the pivot in its place between the partitions
std::swap( vec[ p_index ], vec[ low ] );
return low;
}
void quicksort_range( std::vector< int > &vec, int low, int high )
{
if ( high - low <= 1 )
return;
int pivot = vec[ low ]; /* whatever */
int p_index = partition( vec, low, high, pivot );
quicksort_range( vec, low, p_index );
quicksort_range( vec, p_index + 1, high );
}
void quicksort( std::vector< int > &vec )
{
quicksort_range( vec, 0, vec.size() );
}
#include "test_main.cpp"
S.1.9 [01.r6_radix]
#define UNIT r6_radix
#include <vector>
#include "test_main.cpp"
int digit( unsigned num, int digit, int base )
{
while ( digit --> 0 ) num /= base;
return num % base;
}
int digit_count( unsigned num, int base )
{
int digits = 0;
while ( num )
{
++ digits;
num /= base;
}
return digits;
}
void sort_by_digit( std::vector< unsigned > &to_sort,
int position, int base )
{
PB161 Programming in C++ 87/114 June 28, 2022
std::vector< int > b_size( base, 0 ),
b_start( base, 0 ),
b_index( base, 0 );
std::vector< unsigned > sorted( to_sort.size() );
for ( int num : to_sort )
b_size[ digit( num, position, base ) ] ++;
for ( int i = 1; i < base; ++i )
b_start[ i ] = b_start[ i - 1 ] + b_size[ i - 1 ];
for ( int num : to_sort )
{
int d = digit( num, position, base );
sorted[ b_start[ d ] + b_index[ d ] ] = num;
++ b_index[ d ];
}
std::swap( to_sort, sorted );
}
void radixsort( std::vector< unsigned > &to_sort, int base )
{
if ( to_sort.empty() )
return;
unsigned max = *std::max_element( to_sort.begin(), to_sort.end()
);
int max_digits = digit_count( max, base );
for ( int d = 0; d < max_digits; ++d )
sort_by_digit( to_sort, d, base );
}
Part S.2: Week 2
S.2.1 [02.e1_fibonacci]
#define UNIT e1_fibonacci
#include <vector>
void fibonacci( std::vector< int > &v, int n )
{
v.clear();
if ( n > 0 ) v.push_back( 1 );
if ( n > 1 ) v.push_back( 1 );
for ( int i = 2; i < n; ++ i )
v.push_back( v[ i - 1 ] + v[ i - 2 ] );
}
#include "test_main.cpp"
S.2.2 [02.e2_normalize]
#define UNIT e2_normalize
#include <utility> /* swap */
#include <algorithm> /* min, max */
void normalize( int &p, int &q )
{
int a = std::max( p, q ),
b = std::min( p, q );
while ( b > 0 )
{
a = a % b;
std::swap( a, b );
}
p /= a;
q /= a;
}
#include "test_main.cpp"
S.2.3 [02.e3_accumulate]
#define UNIT e3_accumulate
#include <vector>
auto accumulate = []( auto f, const std::vector< int > &vec )
{
int sum = 0;
for ( int x : vec )
sum += f( x );
return sum;
};
#include "test_main.cpp"
S.2.4 [02.r1_euler]
#define UNIT r1_euler
#include "test_main.cpp"
long phi( long n )
{
long r = n;
long p = 2;
while ( p <= n )
{
if ( n % p == 0 )
{
r *= p - 1;
r /= p;
}
while ( n % p == 0 )
n /= p;
++ p;
}
return r;
}
S.2.5 [02.r2_approx]
#define UNIT r2_approx
#include <cmath>
auto approx = []( auto f, double initial, double prec )
{
double x = f( initial ), y;
do
{
y = x;
x = f( x );
} while ( std::fabs( x - y ) > prec );
return x;
};
double golden( double prec )
{
int a = 1, b = 1;
auto improve = [&]( double )
{
int c = a + b;
a = b;
b = c;
return double( b ) / a;
PB161 Programming in C++ 88/114 June 28, 2022
};
return approx( improve, 1, prec );
}
#include "test_main.cpp"
S.2.6 [02.r3_solve]
#define UNIT r3_solve
#include "test_main.cpp"
#include <algorithm>
bool recurse( int pos, std::vector< bool > &visited,
const std::vector< int > &jumps )
{
if ( pos == int( jumps.size() ) )
{
int cnt = std::count( visited.begin(), visited.end(),
true );
return int( jumps.size() ) == cnt;
}
if ( pos < 0 || pos >= int( visited.size() ) || visited[ pos ] )
return false;
visited[ pos ] = true;
bool won = recurse( pos - jumps[ pos ], visited, jumps ) ||
recurse( pos + jumps[ pos ], visited, jumps );
visited[ pos ] = false;
return won;
}
bool solve( std::vector< int > jumps )
{
std::vector< bool > visited( jumps.size(), false );
return recurse( 0, visited, jumps );
}
S.2.7 [02.r4_sort]
#define UNIT r4_sort
#include <vector>
#include <algorithm>
auto selectsort = []( std::vector< int > &to_sort, auto cmp )
{
for ( auto i = to_sort.begin(); i != to_sort.end(); ++ i )
std::swap( *i, *std::min_element( i, to_sort.end(), cmp ) );
};
#include "test_main.cpp"
S.2.8 [02.r5_permute]
#define UNIT r5_permute
#include "test_main.cpp"
#include <algorithm>
unsigned from_digits( const std::vector< unsigned > &digits, int
base )
{
unsigned r = 0;
for ( unsigned d : digits )
{
r *= base;
r += d;
}
return r;
}
std::vector< unsigned > permute_digits( unsigned n, int base )
{
std::set< unsigned > r;
auto digits = to_digits( n, base );
std::sort( digits.begin(), digits.end() );
do
r.insert( from_digits( digits, base ) );
while ( std::next_permutation( digits.begin(), digits.end() ) );
return std::vector< unsigned >( r.begin(), r.end() );
}
S.2.9 [02.r6_bsearch]
#define UNIT r6_bsearch
#include <vector>
auto search = []( std::vector< int > &vec, int val, auto cmp )
{
auto b = vec.begin(), e = vec.end();
while ( b < e ) /* the search interval is not empty */
{
auto mid = b + ( e - b ) / 2;
if ( cmp( val, *mid ) ) e = mid; /* must be in [b, mid) */
else if ( cmp( *mid, val ) ) b = mid + 1; /* must be in (mid, e) */
else
return mid; /* we found it */
}
return vec.end();
};
#include "test_main.cpp"
Part S.3: Week 3
S.3.1 [03.e1_unique]
#define UNIT e1_unique
#include <set>
#include "test_main.cpp"
std::vector< int > unique( const std::vector< int > &v )
{
std::vector< int > out;
std::set< int > seen;
for ( int x : v )
if ( !seen.count( x ) )
{
out.push_back( x );
seen.insert( x );
}
return out;
}
S.3.2 [03.e2_reflexive]
#define UNIT e2_reflexive
#include "test_main.cpp"
relation reflexive( const relation &r )
{
relation out = r;
for ( auto [ x, y ] : r )
{
out.emplace( x, x );
out.emplace( y, y );
}
return out;
}
PB161 Programming in C++ 89/114 June 28, 2022
S.3.3 [03.e3_normalize]
#define UNIT e3_normalize
#include "test_main.cpp"
signal_t normalize( const signal_t &s )
{
double m = 0;
signal_t out;
for ( double x : s )
m = std::max( m, x );
if ( m == 0 )
m = 1;
for ( double x : s )
out.push_back( x / m );
return out;
}
S.3.4 [03.r1_mode]
#define UNIT r1_mode
#include "test_main.cpp"
#include <map>
int mode( const std::vector< int > &in )
{
std::map< int, int > freq;
int max_val = 0, max_freq = 0;
for ( int x : in )
freq[ x ] ++;
for ( auto [ v, f ] : freq )
if ( f > max_freq )
{
max_val = v;
max_freq = f;
}
return max_val;
}
S.3.5 [03.r2_buckets]
#define UNIT r2_buckets
#include "test_main.cpp"
#include <map>
std::vector< int > sort( const std::vector< int > &stones,
const std::vector< bucket > &buckets )
{
std::vector< int > out( buckets.size(), 0 );
for ( int s : stones )
for ( size_t i = 0; i < buckets.size(); ++ i )
{
auto [ min, max ] = buckets[ i ];
if ( s >= min && s <= max )
out[ i ] += s;
}
return out;
}
S.3.6 [03.r3_shortest]
#define UNIT r3_shortest
#include "test_main.cpp"
#include <queue>
std::map< int, int > shortest( const graph &g, int initial )
{
std::map< int, int > dist;
std::queue< int > queue;
queue.push( initial );
dist[ initial ] = 0;
while ( !queue.empty() )
{
int from = queue.front();
queue.pop();
for ( auto to : g.at( from ) )
{
if ( dist.count( to ) )
continue;
dist[ to ] = dist[ from ] + 1;
queue.push( to );
}
}
return dist;
}
S.3.7 [03.r4_flood]
#define UNIT r4_flood
#include <queue>
#include "test_main.cpp"
int flood( const grid &pixels, int width,
int x0, int y0, bool fill )
{
grid work = pixels;
int count = 0;
int height = pixels.size() / width;
std::queue< std::pair< int, int > > todo;
auto flip = [&]( int x, int y )
{
int idx = y * width + x;
if ( x >= 0 && x < width &&
y >= 0 && y < height && work[ idx ] != fill )
{
todo.emplace( x, y );
work[ idx ] = fill;
++ count;
}
};
flip( x0, y0 );
while ( !todo.empty() )
{
auto [ x, y ] = todo.front();
todo.pop();
for ( int dx : { -1, 0, 1 } )
for ( int dy : { -1, 0, 1 } )
if ( dx || dy )
flip( x + dx, y + dy );
}
return count;
}
S.3.8 [03.r5_colour]
#define UNIT r5_colour
#include <set>
#include <map>
#include <cstdint>
PB161 Programming in C++ 90/114 June 28, 2022
using graph = std::set< std::pair< int, int > >;
bool has_3colouring( const graph &g, std::map< int, int8_t >
&colouring )
{
for ( auto [ u, v ] : g )
if ( colouring[ u ] && colouring[ u ] == colouring[ v ] )
return false;
for ( auto [ u, v ] : g )
if ( !colouring[ v ] )
{
for ( int c = 1; c <= 3; ++ c )
if ( colouring[ u ] != c )
{
colouring[ v ] = c;
if ( has_3colouring( g, colouring ) )
return true;
colouring[ v ] = 0;
}
return false;
}
return true;
}
bool has_3colouring( const graph &g )
{
std::map< int, int8_t > colouring{ { g.begin()->first, 1 } };
return has_3colouring( g, colouring );
}
#include "test_main.cpp"
S.3.9 [03.r6_life]
#define UNIT r6_life
#include "test_main.cpp"
bool updated( int x, int y, const grid &cells )
{
int count = 0;
bool alive = cells.count( { x, y } );
for ( int dx : { -1, 0, 1 } )
for ( int dy : { -1, 0, 1 } )
if ( dx || dy )
count += cells.count( { x + dx, y + dy } );
return alive ? count == 2 || count == 3 : count == 3;
}
grid life( const grid &cells, int n )
{
if ( n == 0 )
return cells;
grid todo, ngen;
for ( auto [ x, y ] : cells )
for ( int dx : { -1, 0, 1 } )
for ( int dy : { -1, 0, 1 } )
todo.emplace( x + dx, y + dy );
for ( auto [ x, y ] : todo )
if ( updated( x, y, cells ) )
ngen.emplace( x, y );
return life( ngen , n - 1 );
}
Part S.4: Week 4
S.4.1 [04.e1_diameter]
#define UNIT e1_diameter
#include <cmath>
struct point
{
double x, y;
point( double x, double y ) : x( x ), y( y ) {}
};
struct circle_radius
{
point center;
double radius;
circle_radius( point c, double r ) : center( c ), radius( r ) {}
};
struct circle_point
{
point center, perimeter;
circle_point( point c, point p )
: center( c ), perimeter( p )
{}
};
double diameter( const circle_radius &c )
{
return c.radius * 2;
}
double diameter( const circle_point &c )
{
double dx = c.center.x - c.perimeter.x;
double dy = c.center.y - c.perimeter.y;
return 2 * std::sqrt( dx * dx + dy * dy );
}
#include "test_main.cpp"
S.4.2 [04.e2_circle]
#define UNIT e2_circle
#include <cmath>
struct point
{
double x, y;
point( double x, double y ) : x( x ), y( y ) {}
};
struct circle
{
point center;
double radius;
circle( point c, double r )
: center( c ), radius( r )
{}
circle( point c, point p )
: center( c ),
radius( std::sqrt( std::pow( p.x - c.x, 2 ) +
std::pow( p.y - c.y, 2 ) ) )
{}
};
#include "test_main.cpp"
S.4.3 [04.e3_index]
PB161 Programming in C++ 91/114 June 28, 2022
#define UNIT e3_index
#include <vector>
#include <utility>
int &element( std::vector< int > &v, int idx )
{
return v[ idx ];
}
int element( const std::vector< int > &v, int idx )
{
return v[ idx ];
}
int &element( std::pair< int, int > &v, int idx )
{
return idx == 0 ? v.first : v.second;
}
int element( const std::pair< int, int > &v, int idx )
{
return idx == 0 ? v.first : v.second;
}
int size( const std::pair< int, int > & ) { return 2; }
int size( const std::vector< int > &v ) { return v.size(); }
#include "test_main.cpp"
S.4.4 [04.r1_complex]
#define UNIT r1_complex
#include <cmath>
struct angle { double v; };
struct complex
{
double real, imag;
complex( double r, double i )
: real( r ), imag( i )
{}
complex( double m, angle phi )
: real( m * std::cos( phi.v ) ),
imag( m * std::sin( phi.v ) )
{}
};
double magnitude( double x )
{
return std::fabs( x );
}
double norm( complex c )
{
return c.real * c.real + c.imag * c.imag;
}
double magnitude( complex c )
{
return std::sqrt( norm( c ) );
}
double reciprocal( double x )
{
return 1 / x;
}
complex reciprocal( complex c )
{
return complex( c.real / norm( c ),
-c.imag / norm( c ) );
}
double arg( complex c )
{
return std::atan2( c.real, c.imag );
}
double real( complex c ) { return c.real; }
double imag( complex c ) { return c.imag; }
#include "test_main.cpp"
S.4.5 [04.r2_bsearch]
#define UNIT r2_bsearch
#include <vector>
using intvec = std::vector< int >;
int bsearch_idx( const intvec &vec, int val )
{
auto b = vec.begin(), e = vec.end();
while ( b < e ) /* the search interval is not empty */
{
auto mid = b + ( e - b ) / 2;
if ( val < *mid ) e = mid; /* must be in [b, mid) */
if ( val > *mid ) b = mid + 1; /* must be in (mid, e) */
if ( val == *mid )
return std::distance( vec.begin(), mid ); /* we found it */
}
return vec.size();
}
auto bsearch( const intvec &vec, int val )
{
return std::next( vec.begin(), bsearch_idx( vec, val ) );
}
auto bsearch( intvec &vec, int val )
{
return std::next( vec.begin(), bsearch_idx( vec, val ) );
}
#include "test_main.cpp"
S.4.6 [04.r3_search]
#define UNIT r3_search
#include <vector>
struct node
{
int value;
int left = -1, right = -1;
node( int v ) : value( v ) {}
};
using node_pool = std::vector< node >;
class node_ref
{
const node_pool &pool;
int idx;
friend class tree;
public:
node_ref( const node_pool &p, int i ) : pool( p ), idx( i ) {}
node_ref left() const { return { pool, pool[ idx ].left }; }
node_ref right() const { return { pool, pool[ idx ].right }; }
int value() const { return pool[ idx ].value; }
bool valid() const { return idx >= 0; }
};
class tree
{
PB161 Programming in C++ 92/114 June 28, 2022
node_pool _pool;
int _root = -1;
public:
node_ref root() const { return { _pool, _root }; }
bool empty() const { return _root == -1; }
node &get( node_ref n ) { return _pool[ n.idx ]; }
void insert( node_ref what, node_ref where, int &attach )
{
if ( !where.valid() )
attach = what.idx;
else if ( what.value() < where.value() )
return insert( what, where.left(), get( where ).left );
else
return insert( what, where.right(), get( where ).right
);
}
void insert( int v )
{
int id = _pool.size();
_pool.emplace_back( v );
return insert( { _pool, id }, root(), _root );
}
};
#include "test_main.cpp"
S.4.7 [04.r4_bitptr]
#define UNIT r4_bitptr
#include <cstddef>
#include <cassert>
class bitptr
{
std::byte *_ptr;
int _offset;
bool _valid = true;
public:
bitptr() : _valid( false ) {}
bitptr( std::byte *p, int o ) : _ptr( p ), _offset( o )
{
assert( o >= 0 && o <= 7 );
}
static auto one() { return std::byte( 1 ); }
bool get() const { return bool( *_ptr & one() << _offset ); }
void set( bool b ) const
{
*_ptr = ( *_ptr & ~( one() << _offset ) ) |
std::byte( b ) << _offset;
}
void advance( int n = 1 ) { _offset += n; _ptr += _offset / 8;
_offset %= 8; }
bool valid() const { return _valid; }
};
class const_bitptr
{
bitptr _ptr;
public:
const_bitptr() = default;
const_bitptr( const std::byte *p, int o )
: _ptr( const_cast< std::byte * >( p ), o )
{}
bool get() const { return _ptr.get(); }
void set( bool b ) const { return _ptr.set( b ); }
void advance( int n = 1 ) { _ptr.advance( n ); }
bool valid() const { return _ptr.valid(); }
};
#include "test_main.cpp"
S.4.8 [04.r6_sort]
#define UNIT r6_sort
#include <vector>
#include <list>
#include <cassert>
int *partition( int *low, const int *high, int pivot )
{
while ( *low < pivot ) /* the pivot must be in there */
++ low;
int *p_ptr = low;
shuffle anything < pivot to the front while remembering where (in the
second half) we stashed the pivot itself
for ( int *p = low + 1; p < high; ++p )
{
if ( *p < pivot )
std::swap( *low++, *p );
if ( *p == pivot )
p_ptr = p;
}
put the pivot in its place between the partitions
std::swap( *p_ptr, *low );
return low;
}
void quicksort( int *low, int *high )
{
if ( high - low <= 1 )
return;
int pivot = *low; /* whatever */
int *p_ptr = partition( low, high, pivot );
quicksort( low, p_ptr );
quicksort( p_ptr + 1, high );
}
void sort( std::vector< int > &vec )
{
quicksort( &*vec.begin(), &*vec.end() );
}
void sort( std::list< int > &list )
{
if ( std::size( list ) <= 1 )
return;
std::list< int > half;
half.splice( half.begin(), list,
list.begin(),
std::next( list.begin(), list.size() / 2 ) );
sort( half );
sort( list );
list.merge( half );
}
#include "test_main.cpp"
PB161 Programming in C++ 93/114 June 28, 2022
Part S.5: Week 5
S.5.1 [05.e1_cartesian]
#define UNIT e1_cartesian
This is a solution that uses the friend syntax. For a solution which uses
the method syntax, see complex.alt.cpp.
class complex
{
double real, imag;
public:
complex( double r, double i ) : real( r ), imag( i ) {}
friend complex operator+( complex a, complex b )
{
You may not know this syntax yet. In a return statement, braces
without a type name call the constructor of the return type. I.e. {
a, b } in this context is the same as complex( a, b ).
return { a.real + b.real, a.imag + b.imag };
}
friend complex operator-( complex a, complex b )
{
return { a.real - b.real, a.imag - b.imag };
}
friend complex operator-( complex a )
{
return { -a.real, -a.imag };
}
friend bool operator==( complex a, complex b )
{
return a.real == b.real && a.imag == b.imag;
}
};
To avoid having a copy of the tests, we #include the original .cpp file
here. You won’t be able to compile this solution if you add your implementation
to the original .cpp file, but you can probably trust us that
the solution above works.
#include "test_main.cpp"
S.5.2 [05.e2_force]
#define UNIT e2_force
#include <cmath>
class force
{
double x, y, z; /* cartesian components of the force */
public:
force( double x, double y, double z )
: x( x ), y( y ), z( z ) {}
We only define multiplication by a scalar (double) from left, since we
only need that here, but it would be equally valid to flip the operand
types (and define scalar multiplication on the right).
friend force operator*( double s, force f )
{
return { s * f.x, s * f.y, s * f.z };
}
Bog-standard vector addition.
friend force operator+( force a, force b )
{
return { a.x + b.x, a.y + b.y, a.z + b.z };
}
Fuzzy vector equality. Two vectors are equal when all their components
are equal.
friend bool operator==( force a, force b )
{
return std::fabs( a.x - b.x ) < 1e-10 &&
std::fabs( a.y - b.y ) < 1e-10 &&
std::fabs( a.z - b.z ) < 1e-10;
}
};
#include "test_main.cpp"
S.5.3 [05.e3_forcefmt]
#define UNIT e3_forcefmt
#include <sstream>
#include <cmath>
class force
{
double x = 0, y = 0, z = 0;
public:
force( double x, double y, double z )
: x( x ), y( y ), z( z )
{}
force() = default;
bool operator==( const force &f ) const
{
return std::fabs( f.x - x ) < 1e-10 &&
std::fabs( f.y - y ) < 1e-10 &&
std::fabs( f.z - z ) < 1e-10;
}
friend std::ostream &operator<<( std::ostream &o,
const force &f )
{
return o << "[" << f.x << " " << f.y << " " << f.z << "]";
}
friend std::istream &operator>>( std::istream &i, force &f )
{
char ch;
if ( !( i >> ch ) || ch != '[' )
i.setstate( i.failbit );
i >> f.x >> f.y >> f.z;
if ( !( i >> ch ) || ch != ']' )
i.setstate( i.failbit );
return i;
}
};
#include "test_main.cpp"
S.5.4 [05.r1_poly]
#define UNIT r1_poly
#include <vector>
class poly
{
std::vector< int > cs;
public:
void set( int p, int c )
PB161 Programming in C++ 94/114 June 28, 2022
{
cs.resize( std::max( degree(), p + 1 ), 0 );
cs[ p ] = c;
}
int get( int p ) const
{
return p < degree() ? cs[ p ] : 0;
}
int degree() const { return cs.size(); }
poly operator+( const poly &o ) const
{
poly rv;
for ( int i = 0; i < std::max( degree(), o.degree() ); ++i )
rv.set( i, get( i ) + o.get( i ) );
return rv;
}
poly operator*( const poly &o ) const
{
poly rv;
for ( int i = 0; i < degree(); ++i )
for ( int j = 0; j < o.degree(); ++j )
rv.set( i + j,
rv.get( i + j ) + get( i ) * o.get( j ) );
return rv;
}
bool operator==( const poly &o ) const
{
for ( int i = 0; i < std::max( degree(), o.degree() ); ++i )
if ( get( i ) != o.get( i ) )
return false;
return true;
}
};
#include "test_main.cpp"
S.5.5 [05.r2_csv]
#define UNIT r2_csv
It is probably easiest to implement this using std::getline to fetch both
lines and individual cells. Other approaches are certainly possible
though.
#include <sstream>
#include <iostream>
#include <vector>
class bad_format {};
class csv
{
std::vector< std::vector< int > > data;
public:
Process a single line, with some rudimentary format validation. The
std::stoi call will throw if the number cannot be parsed, but will not
complain about trailing garbage.
void process_line( const std::string &line, int cols )
{
std::istringstream i_line( line );
std::string cell;
data.emplace_back();
for ( int i = 0; i < cols; ++i )
{
if ( !std::getline( i_line, cell, ',' ) )
throw bad_format();
data.back().push_back( std::stoi( cell ) );
}
i_line.get();
if ( !i_line.eof() )
throw bad_format();
}
The constructor, fetches lines until it reaches the end of the file and
processes each of them using the above.
csv( std::istream &i, int cols )
{
std::string line;
while ( std::getline( i, line ) )
process_line( line, cols );
}
The indexing operator. Since we want [ x ][ y ] to work, we need
to return something with an indexing operator of its own here. The
easiest thing to do is to return the underlying vector in which we store
the row. It would be possible to return a proxy object too.
std::vector< int > &operator[]( int i )
{
return data[ i ];
}
};
#include "test_main.cpp"
S.5.6 [05.r3_set]
#define UNIT r3_set
#include <set>
#include <algorithm>
class set
{
std::set< int > s;
public:
void add( int x ) { s.insert( x ); }
bool has( int x ) const { return s.find( x ) != s.end(); }
set operator|( const set &o ) const
{
set r;
std::set_union( s.begin(), s.end(),
o.s.begin(), o.s.end(),
std::inserter( r.s, r.s.begin() ) );
return r;
}
set operator&( const set &o ) const
{
set r;
std::set_intersection( s.begin(), s.end(),
o.s.begin(), o.s.end(),
std::inserter( r.s, r.s.begin() ) );
return r;
}
set operator-( const set &o ) const
{
set r;
std::set_difference( s.begin(), s.end(),
o.s.begin(), o.s.end(),
std::inserter( r.s, r.s.begin() ) );
return r;
}
PB161 Programming in C++ 95/114 June 28, 2022
bool operator<=( const set &o ) const
{
return ( *this - o ).s.empty();
}
};
#include "test_main.cpp"
S.5.7 [05.r5_json]
#define UNIT r5_json
#include "test_main.cpp"
#include <sstream>
std::string escape( const std::string &in )
{
std::ostringstream ostr;
for ( char c : in )
{
if ( c == '\\' || c == '"' )
ostr << "\\";
ostr << c;
}
return ostr.str();
}
std::string to_json( const str_dict &dict )
{
std::ostringstream ostr;
ostr << "{";
bool comma = false;
for ( auto [ k, v ] : dict )
{
ostr << ( comma ? ", " : " " );
comma = true;
ostr << "\"" << escape( k ) << "\": \"" << escape( v ) <<
"\"";
}
ostr << ( comma ? " }" : "}" );
return ostr.str();
}
S.5.8 [05.r6_cpp]
#define UNIT r6_cpp
#include "test_main.cpp"
#include <string>
#include <fstream>
#include <set>
#include <stack>
inline auto split( const std::string &sv, char delim )
{
if ( auto offset = sv.find( delim ); offset != sv.npos )
return std::pair( sv.substr( 0, offset ), sv.substr( offset
+ 1, sv.npos ) );
else
return std::pair( sv, std::string() );
}
class preprocessor
{
std::set< std::string > defs;
std::stack< bool > _emit;
public:
std::string out;
bool emit() const { return _emit.empty() || _emit.top(); }
void process( const std::string &line )
{
auto [ dir, args ] = split( line, ' ' );
if ( dir == "#ifdef" )
_emit.push( defs.count( args ) );
if ( dir == "#endif" )
_emit.pop();
if ( emit() )
{
if ( dir == "#define" )
defs.insert( args );
if ( dir == "#undef" )
defs.erase( args );
if ( dir == "#include" )
read( args.substr( 1, args.size() - 2 ) );
}
}
void read( const std::string &filename )
{
std::ifstream in( filename ); /* NB. Fails quietly. */
std::string line;
while ( std::getline( in, line ) )
if ( !line.empty() && line[ 0 ] == '#' )
process( line );
else if ( emit() )
out += line + "\n";
}
};
std::string cpp( const std::string &filename )
{
preprocessor p;
p.read( filename );
return p.out;
}
Part S.6: Week 6
S.6.1 [06.e1_default]
#define UNIT e1_default
#include <string>
#include <stdexcept>
int stoi_or( std::string s, int def )
{
try
{
return std::stoi( s );
}
catch ( std::out_of_range & )
{
return def;
}
catch ( std::invalid_argument & )
{
return def;
}
}
#include "test_main.cpp"
S.6.2 [06.e2_counter]
#define UNIT e2_counter
PB161 Programming in C++ 96/114 June 28, 2022
struct counted
{
counted();
counted( const counted & );
~counted();
};
#include "test_main.cpp"
counted::counted()
{
++ counter;
}
counted::counted( const counted & )
{
++ counter;
}
counted::~counted()
{
-- counter;
}
S.6.3 [06.e3_coffee]
#define UNIT e3_coffee
class token
{
bool valid = false;
friend class machine;
public:
token() = default;
token( const token & ) = delete;
token( token &&o ) : valid( o.valid )
{
o.valid = false;
}
token &operator=( const token & ) = delete;
token &operator=( token &&o ) noexcept
{
valid = o.valid;
o.valid = false;
return *this;
}
};
class machine
{
bool busy = false;
public:
token make();
void fetch( token &t );
};
#include "test_main.cpp"
token machine::make()
{
if ( busy )
throw ::busy();
token t;
t.valid = true;
busy = true;
return t;
}
void machine::fetch( token &t )
{
assert( busy );
if ( !t.valid )
throw invalid();
t.valid = false;
}
S.6.4 [06.r1_printing]
#define UNIT r1_printing
#include <string>
#include <map>
class job
{
int _id;
std::string _owner;
int _pages;
public:
job( int id, std::string owner, int pages )
: _id( id ), _owner( owner ), _pages( pages )
{}
job( job && ) = default;
job( const job & ) = delete;
job &operator=( const job & ) = delete;
int id() const { return _id; }
int page_count() const { return _pages; }
std::string owner() const { return _owner; }
};
class queue
{
std::map< int, job > _jobs;
int _count = 0;
public:
int dequeue()
{
const auto &item = *_jobs.begin();
int id = item.first;
_count -= item.second.page_count();
_jobs.erase( id );
return id;
}
void enqueue( job &&j )
{
int id = j.id();
_count += j.page_count();
_jobs.emplace( id, std::move( j ) );
}
job release( int id )
{
job rv( std::move( _jobs.at( id ) ) );
_jobs.erase( id );
_count -= rv.page_count();
return rv;
}
int page_count() const
{
return _count;
}
};
#include "test_main.cpp"
S.6.5 [06.r2_bsearch]
PB161 Programming in C++ 97/114 June 28, 2022
#define UNIT r2_bsearch
#include <vector>
#include <string>
class token;
class flat_map
{
std::vector< std::pair< std::string, token > > _data;
public:
bool emplace( std::string k, int v );
int index( const std::string &k ) const;
int index_or_throw( const std::string &k ) const;
token &at( const std::string &k );
const token &at( const std::string &k ) const;
token &operator[]( const std::string &k );
};
#include "test_main.cpp"
int flat_map::index( const std::string &k ) const
{
int low = 0, high = _data.size();
while ( low < high )
{
int mid = ( low + high ) / 2;
if ( k < _data[ mid ].first )
high = mid;
else if ( k > _data[ mid ].first )
low = mid + 1;
else
return mid;
}
assert( low <= int( _data.size() ) );
return low;
}
bool flat_map::emplace( std::string k, int v )
{
int idx = index( k );
if ( idx < int( _data.size() ) && _data[ idx ].first == k )
return false;
_data.emplace( _data.begin() + idx, std::move( k ), v );
return true;
}
int flat_map::index_or_throw( const std::string &k ) const
{
if ( int idx = index( k ); _data[ idx ].first == k )
return idx;
else
throw std::out_of_range( "indexing flat_map" );
}
token &flat_map::at( const std::string &k )
{
return _data[ index_or_throw( k ) ].second;
}
const token &flat_map::at( const std::string &k ) const
{
return _data[ index_or_throw( k ) ].second;
}
token &flat_map::operator[]( const std::string &k )
{
if ( int idx = index( k ); _data[ idx ].first == k )
return _data[ idx ].second;
emplace( k, 0 );
return at( k );
}
S.6.6 [06.r4_tinyvec]
#define UNIT r4_tinyvec
#include <array>
#include <memory>
class token;
class tiny_vector
{
std::array< uint8_t, 32 > _mem;
int _count = 0;
public:
void insert( int idx, token &&v );
void erase( int idx );
token *slot( int i );
const token *slot( int i ) const;
const token &front() const { return *slot( 0 ); }
const token &back() const { return *slot( _count - 1 ); }
token &front() { return *slot( 0 ); }
token &back() { return *slot( _count - 1 ); }
~tiny_vector();
};
#include "test_main.cpp"
token *tiny_vector::slot( int i )
{
assert( i >= 0 );
assert( i < _count );
return reinterpret_cast< token * >( _mem.begin() ) + i;
}
const token *tiny_vector::slot( int i ) const
{
return reinterpret_cast< const token * >( _mem.begin() ) + i;
}
tiny_vector::~tiny_vector()
{
while ( _count )
erase( _count - 1 );
}
void tiny_vector::erase( int idx )
{
std::destroy_at( slot( idx ) );
for ( int i = idx; i < _count - 1; ++i )
{
std::uninitialized_move_n( slot( i + 1 ), 1, slot( i ) );
std::destroy_at( slot( i + 1 ) );
}
-- _count;
}
void tiny_vector::insert( int idx, token &&v )
{
if ( _count == _mem.size() / sizeof( token ) )
throw insufficient_space();
++ _count;
for ( int i = _count - 1; i > idx; --i )
{
std::uninitialized_move_n( slot( i - 1 ), 1, slot( i ) );
PB161 Programming in C++ 98/114 June 28, 2022
std::destroy_at( slot( i - 1 ) );
}
if ( idx < _count - 1 )
std::destroy_at( slot( idx ) );
std::uninitialized_move_n( &v, 1, slot( idx ) );
}
S.6.7 [06.r5_lock]
#define UNIT r5_lock
class mutex;
class lock
{
mutex *_mutex;
public:
lock( mutex &m );
~lock();
lock( const lock & ) = delete;
lock &operator=( const lock & ) = delete;
lock( lock && );
lock &operator=( lock && );
};
#include "test_main.cpp"
lock::lock( mutex &m )
: _mutex( &m )
{
_mutex->lock();
}
lock::~lock()
{
if ( _mutex )
_mutex->unlock();
}
lock::lock( lock &&o )
: _mutex( o._mutex )
{
o._mutex = nullptr;
}
lock &lock::operator=( lock &&o )
{
if ( _mutex )
_mutex->unlock();
_mutex = o._mutex;
o._mutex = nullptr;
return *this;
}
S.6.8 [06.r6_bounded]
#define UNIT r6_bounded
#include <vector>
class insufficient_space {};
class bounded_queue
{
std::vector< int > _data;
int _first = 0, _count = 0;
public:
explicit bounded_queue( int cnt ) : _data( cnt ) {}
bool empty() const { return !_count; }
bool full() const { return _count == int( _data.size() ); }
int next() const { return _data[ _first ]; }
int pop()
{
int rv = _data[ _first ++ ];
_first %= _data.size();
-- _count;
return rv;
}
void push( int v )
{
if ( full() )
throw insufficient_space();
_data[ ( _first + _count ) % _data.size() ] = v;
++ _count;
}
};
#include "test_main.cpp"
Part S.7: Week 7
S.7.1 [07.e1_dynarray]
#define UNIT e1_dynarray
#include <memory>
#include <algorithm>
class dynarray
{
std::unique_ptr< int[] > _data;
int _size;
public:
dynarray( int size )
: _data( std::make_unique< int[] >( size ) ),
_size( size )
{}
void resize( int size )
{
auto d_new = std::make_unique< int[] >( size );
auto d_old = _data.get();
std::copy( d_old, d_old + std::min( size, _size ),
d_new.get() );
_data = std::move( d_new );
_size = size;
}
int &operator[]( int i )
{
return _data[ i ];
}
};
#include "test_main.cpp"
S.7.2 [07.e2_list]
#define UNIT e2_list
#include <memory>
class list
{
int _head;
std::unique_ptr< list > _tail;
public:
list( const list &o )
: _head( o._head ),
_tail( o._tail ? std::make_unique< list >( *o._tail )
: nullptr )
PB161 Programming in C++ 99/114 June 28, 2022
{}
list( int h, const list &t )
: _head( h ),
_tail( std::make_unique< list >( t ) )
{}
list() = default;
bool empty() const { return !_tail; }
int head() const { return _head; }
const list &tail() const { return *_tail; }
};
#include "test_main.cpp"
S.7.3 [07.r1_circular]
#define UNIT r1_circular
The solution proceeds along the lines of queue.cpp: we use a singlylinked
list. The solution is simpler because we do not need iteration
(which was replaced by rotate.
#include <memory>
A node of the data structure, bog standard.
struct circular_node
{
using pointer = std::unique_ptr< circular_node >;
pointer next;
int value;
};
Like before, we remember the head of the list (as a unique_ptr) and a
pointer to the last node, which we need to implement rotate.
class circular
{
std::unique_ptr< circular_node > head;
circular_node *last = nullptr;
public:
bool empty() const { return !last; }
In this case, the push method works at the head, since we use the list
in a stack-like order. We have already seen move assignment, using
the std::move helper function.
void push( int v )
{
auto new_head = std::make_unique< circular_node >();
new_head->value = v;
new_head->next = std::move( head );
head = std::move( new_head );
if ( !last ) last = head.get();
}
Popping items at the head is quite simple.
void pop()
{
head = std::move( head->next );
if ( !head ) last = nullptr;
}
Access to the top element.
int top() const { return head->value; }
int &top() { return head->value; }
And the rotate operation: we pop a node off the head and chain it to
the list at the tail end. Must not forget to update the last pointer. Does
not work on empty list.
void rotate()
{
auto next_head = std::move( head->next );
last->next = std::move( head );
last = last->next.get();
head = std::move( next_head );
}
};
#include "test_main.cpp"
S.7.4 [07.r2_zipper]
#define UNIT r2_zipper
#include <memory>
#include <cassert>
struct node
{
using ptr = std::unique_ptr< node >;
int value;
ptr next;
node( int v, ptr n ) : value( v ), next( std::move( n ) ) {}
};
class zipper
{
int _focus;
using node_ptr = std::unique_ptr< node >;
node_ptr _left, _right;
public:
zipper( int f ) : _focus( f ) {}
bool shift( node_ptr &a, node_ptr &b )
{
auto new_b = std::move( b->next );
auto new_a = std::move( b );
new_a->next = std::move( a );
std::swap( new_a->value, _focus );
b = std::move( new_b );
a = std::move( new_a );
return true;
}
void push( node_ptr &p, int v )
{
p = std::make_unique< node >( v, std::move( p ) );
}
bool shift_left()
{
return _left ? shift( _right, _left ) : false;
}
bool shift_right()
{
return _right ? shift( _left, _right ) : false;
}
void push_left( int v ) { push( _left, v ); }
void push_right( int v ) { push( _right, v ); }
int &focus() { return _focus; }
int focus() const { return _focus; }
};
#include "test_main.cpp"
PB161 Programming in C++ 100/114 June 28, 2022
S.7.5 [07.r3_segment]
#define UNIT r3_segment
#include <memory>
#include <utility>
#include <cstdlib>
struct segment_map
{
struct node
{
std::unique_ptr< node > l, r;
int div;
node( int d ) : div( d ) {}
};
std::unique_ptr< node > root;
int min, max;
segment_map( int l, int u ) : min( l ), max( u ) {}
std::pair< int, int > query( int i, node *n, int l, int u )
const
{
if ( !n ) return { l, u };
if ( i < n->div ) return query( i, n->l.get(), l, n->div );
if ( i >= n->div ) return query( i, n->r.get(), n->div, u );
std::abort();
}
std::pair< int, int > query( int i ) const
{
return query( i, root.get(), min, max );
}
void split( int n )
{
auto old_root = std::move( root );
root = std::make_unique< node >( n );
if ( !old_root )
return;
if ( old_root->div > n )
root->r = std::move( old_root );
else
root->l = std::move( old_root );
}
};
#include "test_main.cpp"
S.7.6 [07.r4_diff]
#define UNIT r4_diff
#include <memory>
#include <cmath>
struct node
{
using ptr = std::shared_ptr< node >;
enum op_t { cnst, var, add, mul, exp } op;
int num = 0;
ptr l, r;
};
class expr
{
public:
node::ptr ptr;
expr() : ptr( std::make_shared< node >() ) {}
expr( int c ) : expr() { ptr->num = c; ptr->op = node::cnst; }
expr( node::op_t o, node::ptr l = nullptr,
node::ptr r = nullptr )
: expr()
{
ptr->op = o;
ptr->l = l;
ptr->r = r;
}
expr( node::ptr p ) :ptr( p ) {}
friend expr expnat( expr e )
{
return { node::exp, e.ptr };
}
friend expr operator+( expr a, expr b )
{
return { node::add, a.ptr, b.ptr };
}
friend expr operator*( expr a, expr b )
{
return { node::mul, a.ptr, b.ptr };
}
};
const expr x{ node::var };
double eval( expr e, double v )
{
switch ( e.ptr->op )
{
case node::cnst: return e.ptr->num;
case node::var: return v;
case node::add: return eval( e.ptr->l, v ) + eval( e.ptr->r,
v );
case node::mul: return eval( e.ptr->l, v ) * eval( e.ptr->r,
v );
case node::exp: return std::exp( eval( e.ptr->l, v ) );
}
abort();
}
expr diff( expr e )
{
switch ( e.ptr->op )
{
case node::cnst: return { 0 };
case node::var: return { 1 };
case node::add:
return diff( e.ptr->l ) + diff( e.ptr->r );
case node::mul:
return diff( e.ptr->l ) * e.ptr->r +
diff( e.ptr->r ) * e.ptr->l;
case node::exp:
return e * diff( e.ptr->l );
}
abort();
}
#include "test_main.cpp"
Part S.8: Week 8
S.8.1 [08.e1_resistance]
#define UNIT e1_resistance
class segment
{
public:
virtual double r() const = 0;
};
class series : public segment
PB161 Programming in C++ 101/114 June 28, 2022
{
double total = 0;
public:
void add( double r ) { total += r; }
void add( const segment &s ) { total += s.r(); }
double r() const override { return total; }
};
class parallel : public segment
{
double recip = 0;
public:
void add( double r ) { recip += 1.0 / r; }
void add( const segment &s ) { recip += 1.0 / s.r(); }
double r() const override { return 1.0 / recip; }
};
double resistance( const segment &s )
{
return s.r();
}
#include "test_main.cpp"
S.8.2 [08.e2_perimeter]
#define UNIT e2_perimeter
#include <cmath>
class shape
{
public:
virtual double perimeter() const = 0;
};
class circle : public shape
{
double _radius;
public:
circle( double r ) : _radius( r ) {}
double perimeter() const override
{
return 8 * std::atan( 1 ) * _radius;
}
};
class rectangle : public shape
{
double _width, _height;
public:
rectangle( double w, double h ) : _width( w ), _height( h ) {}
double perimeter() const override
{
return 2 * _width + 2 * _height;
}
};
#include "test_main.cpp"
S.8.3 [08.e3_fight]
#define UNIT e3_fight
class rock;
class paper;
class scissors;
class gesture
{
public:
virtual bool visit( const rock & ) const = 0;
virtual bool visit( const paper & ) const = 0;
virtual bool visit( const scissors & ) const = 0;
virtual bool fight( const gesture & ) const = 0;
};
class rock : public gesture
{
bool visit( const rock & ) const override { return false; }
bool visit( const paper & ) const override { return true; }
bool visit( const scissors & ) const override { return false; }
bool fight( const gesture &g ) const override
{
return g.visit( *this );
}
};
class paper : public gesture
{
bool visit( const rock & ) const override { return false; }
bool visit( const paper & ) const override { return false; }
bool visit( const scissors & ) const override { return true; }
bool fight( const gesture &g ) const override
{
return g.visit( *this );
}
};
class scissors : public gesture
{
bool visit( const rock & ) const override { return true; }
bool visit( const paper & ) const override { return false; }
bool visit( const scissors & ) const override { return false; }
bool fight( const gesture &g ) const override
{
return g.visit( *this );
}
};
#include "test_main.cpp"
S.8.4 [08.r1_bom]
#define UNIT r1_bom
#include <memory>
#include <string>
#include <vector>
#include <stdexcept>
The base class. It remembers the part number and provides the required
interface: description and part_no. Do not forget the virtual
destructor!
class part
{
std::string _part_no;
public:
part( std::string pn ) : _part_no( pn ) {}
virtual std::string description() const = 0;
std::string part_no() const { return _part_no; }
virtual ~part() = default;
};
The two derived classes, 80 % boilerplate.
class resistor : public part
{
int _resistance;
public:
resistor( std::string pn, int r )
: part( pn ), _resistance( r )
{}
PB161 Programming in C++ 102/114 June 28, 2022
std::string description() const override
{
return std::string( "resistor " ) +
std::to_string( _resistance ) + "Ω";
}
};
class capacitor : public part
{
int _capacitance;
public:
capacitor( std::string pn, int c )
: part( pn ), _capacitance( c )
{}
std::string description() const override
{
return std::string( "capacitor " ) +
std::to_string( _capacitance ) + "μF";
}
};
The smart pointer to hold and own instances of part.
using part_ptr = std::unique_ptr< part >;
The bom class itself holds the parts using the above pointer. It would
be possible to use std::map too (and also more efficient for longer part
lists). Here, we use an std::vector of pairs, where the pair holds the
part pointer and the quantity. When the item with the given order
number is not on the list, we throw an exception.
class bom
{
using item = std::pair< part_ptr, int >;
std::vector< item > _parts;
Find the item in the list: the common parts of find and qty.
const item &_find( std::string pn ) const
{
for ( const auto &part : _parts )
if ( part.first->part_no() == pn )
return part;
throw std::runtime_error( "part not found" );
}
public:
We don’t bother with duplicates. Notice the std::move though – we
have to transfer the ownership of the part instance to the vector (via
the pair).
void add( part_ptr p, int c )
{
_parts.emplace_back( std::move( p ), c );
}
const part &find( std::string pn ) const
{
return *_find( pn ).first;
}
int qty( std::string pn ) const { return _find( pn ).second; }
};
#include "test_main.cpp"
S.8.5 [08.r2_circuit]
#define UNIT r2_circuit
The base class. We keep track of the inputs using raw pointers, since
we do not own them. We use a protected virtual method to implement
the ‘business logic’ that changes from class to class, while the outside
interface is defined entirely using standard (non-virtual) methods.
class component
{
component *left = nullptr,
*right = nullptr;
protected:
virtual bool eval( bool, bool ) = 0;
public:
void connect( int n, component &c )
{
( n ? right : left ) = &c;
}
bool read()
{
return eval( left ? left->read() : false,
right ? right->read() : false );
}
virtual ~component() = default;
};
The NAND gate and the source component are trivial enough.
class nand : public component
{
bool eval( bool x, bool y ) override { return !( x && y ); }
};
class source : public component
{
bool eval( bool, bool ) override { return true; }
};
The delay component provides one bit of memory. Reading the component
will cause the value to be updated (read always calls eval internally).
This class is also the reason why eval cannot be marked
const.
class delay : public component
{
bool _value = false;
bool eval( bool x, bool ) override
{
bool rv = _value;
_value = x;
return rv;
}
};
#include "test_main.cpp"
S.8.6 [08.r3_loops]
#define UNIT r3_loops
class component
{
int left_i, right_i;
component *left = nullptr,
*right = nullptr;
protected:
virtual bool eval_0( bool, bool ) { return false; }
virtual bool eval_1( bool, bool ) { return false; }
bool get_left() const { return left ? left->read( left_i ) :
false; }
bool get_right() const { return right ? right->read( right_i ) :
false; }
PB161 Programming in C++ 103/114 June 28, 2022
public:
void connect( int i, int o, component &c )
{
( i ? right_i : left_i ) = o;
( i ? right : left ) = &c;
}
virtual bool read( int o )
{
auto l = get_left();
auto r = get_right();
if ( o == 0)
return eval_0( l, r );
else
return eval_1( l, r );
}
virtual ~component() = default;
};
class cnot : public component
{
bool eval_0( bool x, bool ) override { return x; }
bool eval_1( bool x, bool y ) override
{
if ( x )
return y;
else
return !y;
}
};
class nand : public component
{
bool eval_0( bool x, bool y ) override { return !( x && y ); }
bool eval_1( bool x, bool y ) override { return x && y; }
};
class eq : public component
{
bool eval_0( bool x, bool y ) override { return x == y; }
bool eval_1( bool x, bool y ) override { return x != y; }
};
class delay : public component
{
bool _x = false, _y = false;
bool _in_read = false;
bool read( int o ) override
{
bool out = o ? _y : _x;
if ( _in_read )
return out;
_in_read =true;
_x = get_left();
_y = get_right();
_in_read = false;
return out;
}
};
class latch : public component
{
bool _value = false;
bool eval_0( bool x, bool y ) override { return eval( x, y ); }
bool eval_1( bool x, bool y ) override { return !eval( x, y ); }
bool eval( bool x, bool y )
{
if ( !x && y ) _value = true;
if ( x ) _value = false;
return _value;
}
};
#include "test_main.cpp"
S.8.7 [08.r4_pretty]
#define UNIT r4_pretty
class node;
using node_ptr = std::unique_ptr< node >;
class node
{
public:
virtual int precedence() const = 0;
virtual void print( std::stringstream &out,
bool enclose ) const = 0;
std::string print() const
{
std::stringstream out;
print( out, false );
return out.str();
}
virtual ~node() = default;
};
class constant : public node
{
int _value;
public:
constant( int v ) : _value( v ) {}
int precedence() const override { return 100; }
void print( std::stringstream &o, bool enclose ) const override
{
assert( !enclose );
o << _value;
}
};
class binary : public node
{
node_ptr _left, _right;
public:
binary( node_ptr l, node_ptr r )
: _left( std::move( l ) ),
_right( std::move( r ) )
{}
virtual char op_char() const = 0;
void print( std::stringstream &o, bool enclose ) const override
{
if ( enclose )
o << "( ";
_left->print( o, _left->precedence() < precedence() );
o << " " << op_char() << " ";
_right->print( o, _right->precedence() < precedence() );
if ( enclose )
o << " )";
}
};
class equality : public binary
{
public:
using binary::binary;
int precedence() const override { return 1; }
PB161 Programming in C++ 104/114 June 28, 2022
char op_char() const override { return '='; }
};
class addition : public binary
{
public:
using binary::binary;
int precedence() const override { return 2; }
char op_char() const override { return '+'; }
};
class multiplication : public binary
{
public:
using binary::binary;
int precedence() const override { return 3; }
char op_char() const override { return '*'; }
};
#include "test_main.cpp"
S.8.8 [08.r5_json]
#define UNIT r5_json
class node
{
public:
std::string print() const
{
std::stringstream str;
format( str );
return str.str();
}
virtual void format( std::stringstream &out ) const = 0;
virtual ~node() = default;
};
using node_ptr = std::unique_ptr< node >;
class number : public node
{
int _value;
public:
explicit number( int v ) : _value( v ) {}
void format( std::stringstream &out ) const override
{
out << _value;
}
};
auto _print_list = []( const auto &items, auto format,
std::stringstream &out,
char open, char close )
{
bool first = true;
for ( const auto &v : items )
{
out << ( first ? open : ',' ) << " ";
format( v );
first = false;
}
out << ( first ? open : ' ' ) << close;
};
class object : public node
{
std::vector< std::pair< std::string, node_ptr > > _items;
public:
void format( std::stringstream &out ) const override
{
auto format = [&]( const auto &item )
{
const auto &[ key, value ] = item;
out << '"' << key << "\": ";
value->format( out );
};
_print_list( _items, format, out, '{', '}' );
}
void append( std::string s, node_ptr v )
{
_items.emplace_back( s, std::move( v ) );
}
};
class array : public node
{
std::vector< node_ptr > _items;
public:
void format( std::stringstream &out ) const override
{
auto format = [&]( const auto &v ) { v->format( out ); };
_print_list( _items, format, out, '[', ']' );
}
void append( node_ptr v )
{
_items.emplace_back( std::move( v ) );
}
};
#include "test_main.cpp"
S.8.9 [08.r6_while]
class statement;
using state = std::map< std::string, int >;
using stmt_ptr = std::unique_ptr< statement >;
class statement
{
public:
virtual state eval( state s ) const = 0;
virtual ~statement() = default;
};
class stmt_inc : public statement
{
std::string _var;
public:
stmt_inc( std::string v ) : _var( v ) {}
state eval( state s ) const override
{
s[ _var ] ++;
return s;
}
};
class stmt_while : public statement
{
std::string _v_1, _v_2;
stmt_ptr _body;
public:
stmt_while( std::string v1, std::string v2, stmt_ptr b )
: _v_1( v1 ), _v_2( v2 ), _body( std::move( b ) )
{}
state eval( state s ) const override
{
while ( s[ _v_1 ] != s[ _v_2 ] )
PB161 Programming in C++ 105/114 June 28, 2022
s = _body->eval( std::move( s ) );
return s;
}
};
class stmt_block : public statement
{
std::vector< stmt_ptr > _body;
public:
void append( stmt_ptr stmt )
{
_body.emplace_back( std::move( stmt ) );
}
state eval( state s ) const override
{
for ( const auto &stmt : _body )
s = stmt->eval( std::move( s ) );
return s;
}
};
#define UNIT r6_while
#include "test_main.cpp"
Part S.9: Week 9
S.9.1 [09.e1_iota]
#define UNIT e1_iota
template< typename fun_t >
void iota( fun_t f, int start, int end )
{
for ( int i = start; i < end; ++ i )
f( i );
}
#include "test_main.cpp"
S.9.2 [09.e2_quot]
#define UNIT e2_quot
template< typename id_t > /* id for integral domain */
class rat
{
id_t p, q;
public:
rat( id_t p, id_t q ) : p( p ), q( q ) {}
bool operator==( rat r ) const { return p * r.q == r.p * q; }
friend rat operator+( rat a, rat b )
{
return { a.p * b.q + b.p * a.q, a.q * b.q };
}
rat operator*( rat r ) const { return { p * r.p, q * r.q }; }
rat operator/( rat r ) const { return { p * r.q, q * r.p }; }
};
class gauss
{
int r, i;
public:
gauss( int r, int i ) : r( r ), i( i ) {}
gauss operator+( gauss b ) const
{
return { r + b.r, i + b.i };
}
gauss operator*( gauss b ) const
{
return { r * b.r - i * b.i, r * b.i + i * b.r };
}
bool operator==( gauss b ) const
{
return r == b.r && i == b.i;
}
};
#include "test_main.cpp"
S.9.3 [09.e3_split]
#define UNIT e3_split
#include "test_main.cpp"
split_view split( std::string_view s, char delim )
{
size_t idx = s.find( delim );
if ( idx == s.npos )
return { s, "" };
else
return { s.substr( 0, idx ), s.substr( idx + 1, s.npos ) };
}
S.9.4 [09.r1_tfold]
#define UNIT r1_tfold
template< typename value_t >
struct tree;
template< typename fun_t, typename value_t >
value_t tfold( fun_t f, const tree< value_t > &t );
#include "test_main.cpp"
template< typename fun_t, typename value_t >
value_t tfold( fun_t f, const tree< value_t > &t )
{
if ( !t.left )
return t.value;
auto left = tfold( f, *t.left ),
right = tfold( f, *t.right );
return f( f( t.value, left ), right );
}
S.9.5 [09.r2_tmap]
#define UNIT r2_tmap
#include <type_traits>
#include <vector>
template< typename value_t >
struct tree;
template< typename fun_t, typename val_t >
using mapped_tree = tree< std::invoke_result_t< fun_t, val_t > >;
template< typename fun_t, typename val_t >
using mapped_vec =
std::vector< std::invoke_result_t< fun_t, val_t > >;
template< typename fun_t, typename value_t >
mapped_tree< fun_t, value_t >
tmap( fun_t f, const tree< value_t > &t );
#include "test_main.cpp"
template< typename fun_t, typename value_t >
auto map( fun_t f, const std::vector< value_t > &vec )
{
PB161 Programming in C++ 106/114 June 28, 2022
mapped_vec< fun_t, value_t > out;
for ( const auto &v : vec )
out.push_back( f( v ) );
return out;
}
template< typename fun_t, typename value_t >
mapped_tree< fun_t, value_t >
tmap( fun_t f, const tree< value_t > &t )
{
using mt = mapped_tree< fun_t, value_t >;
auto map_sub = [&]( const auto &subtree )
{
return tmap( f, subtree );
};
return mt( f( t.value ), map( map_sub, t.children ) );
}
S.9.6 [09.r3_monoid]
#define UNIT r3_monoid
#include <string>
template< typename hom_t >
struct elem
{
std::string v;
hom_t h;
elem( std::string s, hom_t h ) : v( s ), h( h ) {}
elem operator*( const elem &e ) const { return { v + e.v, h }; }
bool operator==( const elem &e ) const { return h( v ) == h( e.v
); }
};
template< typename hom_t >
class monoid
{
hom_t h;
public:
monoid( hom_t h ) : h( h ) {}
::elem< hom_t > elem( std::string s ) { return { s, h }; }
};
#include "test_main.cpp"
S.9.7 [09.r4_treap]
#define UNIT r4_treap
template< typename key_t >
class treap
{
class node
{
key_t _key;
int _priority;
std::unique_ptr< node > _left, _right;
public:
node( key_t k, int p )
: _key( std::move( k ) ), _priority( p )
{}
int priority() const { return _priority; }
const key_t &key() const { return _key; }
auto &child( bool dir ) { return dir ? _left : _right; }
auto left() const { return _left.get(); }
auto right() const { return _right.get(); }
};
using node_ptr = std::unique_ptr< node >;
static node_ptr rotate( node_ptr self, bool dir )
{
auto root = std::move( self->child( dir ) );
auto detach = std::move( root->child( !dir ) );
assert( root );
self->child( dir ) = std::move( detach );
root->child( !dir ) = std::move( self );
return root;
}
static node_ptr fix( node_ptr self, bool dir )
{
assert( self->child( dir ) );
if ( self->priority() > self->child( dir )->priority() )
return self;
else
return rotate( std::move( self ), dir );
}
static node_ptr insert( node_ptr self, key_t key, int prio )
{
if ( !self )
return std::make_unique< node >( std::move( key ), prio
);
bool dir = key < self->key();
auto &child = self->child( dir );
child = insert( std::move( child ), std::move( key ), prio
);
return fix( std::move( self ), dir );
}
node_ptr _root;
public:
void insert( key_t key, int prio )
{
_root = insert( std::move( _root ),
std::move( key ), prio );
}
const node *root() const { return _root.get(); }
};
#include "test_main.cpp"
S.9.8 [09.r6_finally]
#define UNIT r6_finally
template< typename handler_t >
class finally
{
std::optional< handler_t > _handler;
public:
explicit finally( handler_t h )
: _handler( std::move( h ) )
{}
finally( const finally & ) = delete;
finally &operator=( const finally & ) = delete;
finally( finally &&other )
: _handler( std::move( other._handler ) )
{
other.cancel();
}
finally &operator=( finally && other )
{
PB161 Programming in C++ 107/114 June 28, 2022
if ( other._handler )
_handler.emplace( std::move( *other._handler ) );
other.cancel();
return *this;
}
void cancel() { _handler.reset(); }
~finally()
{
if ( _handler )
( *_handler )();
}
};
#include "test_main.cpp"
Part S.10: Week 10
S.10.1 [10.e1_format]
#define UNIT e1_format
#include <vector>
#include <set>
#include <sstream>
template< typename T >
std::string format( const T &coll, char b, char e )
{
int i = 0;
std::ostringstream str;
for ( const auto &e : coll )
str << ( i++ ? ',' : b ) << " " << e;
if ( i ) str << " " << e; else str << b << e;
return str.str();
}
template< typename T >
std::string format( const std::vector< T > &s )
{
return format( s, '[', ']' );
}
template< typename T >
std::string format( const std::set< T > &s )
{
return format( s, '{', '}' );
}
#include "test_main.cpp"
S.10.2 [10.e2_concat]
#define UNIT e2_concat
#include <vector>
template< typename seq1_t, typename seq2_t >
auto concat( const seq1_t &s1, const seq2_t &s2 )
{
std::vector< typename seq1_t::value_type > out;
for ( const auto &x : s1 )
out.push_back( x );
for ( const auto &x : s2 )
out.push_back( x );
return out;
}
#include "test_main.cpp"
S.10.3 [10.e3_select]
#define UNIT e3_select
#include <vector>
#include <variant>
template< typename seq1_t, typename seq2_t >
auto select( const seq1_t &s1, const seq2_t &s2,
const std::vector< bool > &bmp )
{
using variant = std::variant< typename seq1_t::value_type,
typename seq2_t::value_type >;
std::vector< variant > out;
auto i = s1.begin();
auto j = s2.begin();
for ( bool first : bmp )
{
out.emplace_back( first ? variant( *i ) : variant( *j ) );
++ i, ++ j;
}
return out;
}
#include "test_main.cpp"
S.10.4 [10.r1_icons]
#define UNIT r1_icons
struct null;
template< typename cdr_t >
struct cons
{
int car;
cdr_t cdr;
cons( int car, const cdr_t &cdr ) : car( car ), cdr( cdr ) {}
};
int sum( null );
template< typename cons_t >
int sum( const cons_t & c )
{
return c.car + sum( c.cdr );
}
#include "test_main.cpp"
int sum( null )
{
return 0;
}
S.10.5 [10.r2_sorted]
#define UNIT r2_sorted
#include <any>
struct check_sorted
{
std::any last;
bool mismatch = false;
bool was_sorted() const { return !mismatch; }
template< typename value_t >
void operator()( const value_t &v )
{
if ( last.has_value() )
{
if ( std::any_cast< value_t >( last ) > v )
mismatch = true;
}
last = v;
}
PB161 Programming in C++ 108/114 June 28, 2022
};
#include "test_main.cpp"
S.10.6 [10.r3_fsm]
#define UNIT r3_fsm
#include <string_view>
#include <map>
template< typename letter_t >
class fsm
{
std::map< letter_t, const fsm * > _next;
bool _accept;
public:
explicit fsm( bool a = false ) : _accept( a ) {}
void next( letter_t c, const fsm &n ) { _next[ c ] = &n; }
template< typename seq_t >
bool accept( const seq_t &s ) const
{
return accept( s.begin(), s.end() );
}
template< typename iter_t >
bool accept( iter_t b, iter_t e ) const
{
if ( b == e ) return _accept;
if ( auto n = _next.find( *b ); n != _next.end() )
return n->second->accept( ++b, e );
else
return false;
}
};
#include "test_main.cpp"
S.10.7 [10.r5_bimap]
#define UNIT r5_bimap
template< typename left_t, typename right_t >
class bimap
{
std::map< left_t, const right_t * > _right;
std::map< right_t, const left_t * > _left;
public:
bool insert( left_t l, right_t r )
{
if ( _left.count( r ) || _right.count( l ) )
return false;
auto [ ri, ri_n ] = _right.emplace( std::move( l ), nullptr
);
auto [ li, li_n ] = _left.emplace( std::move( r ), nullptr
);
ri->second = &li->first;
li->second = &ri->first;
return true;
}
template< typename map_t, typename key_t >
static auto get( const map_t &map, const key_t &key )
{
auto it = map.find( key );
return it == map.end() ? nullptr : it->second;
}
const left_t *get_left( const right_t &r ) const
{
return get( _left, r );
}
const right_t *get_right( const left_t &l ) const
{
return get( _right, l );
}
void erase( const left_t &l, const right_t &r )
{
_left.erase( r );
_right.erase( l );
}
};
#include "test_main.cpp"
S.10.8 [10.r6_tinyvec]
#define UNIT r6_tinyvec
#include <array>
#include <memory>
#include <cassert>
class insufficient_space;
void throw_insufficient_space();
template< typename value_t, size_t max_size >
class tiny_vector
{
std::array< uint8_t, max_size * sizeof( value_t ) > _mem;
int _count = 0;
public:
value_t *slot( int i )
{
assert( i >= 0 );
assert( i < _count );
return reinterpret_cast< value_t * >( _mem.begin() ) + i;
}
const value_t *slot( int i ) const
{
return reinterpret_cast< const value_t * >( _mem.begin() ) +
i;
}
~tiny_vector()
{
while ( _count )
erase( _count - 1 );
}
void erase( int idx )
{
std::destroy_at( slot( idx ) );
for ( int i = idx; i < _count - 1; ++i )
{
std::uninitialized_move_n( slot( i + 1 ), 1, slot( i )
);
std::destroy_at( slot( i + 1 ) );
}
-- _count;
}
void insert( int idx, value_t &&v )
{
if ( _count == max_size )
throw_insufficient_space();
PB161 Programming in C++ 109/114 June 28, 2022
++ _count;
for ( int i = _count - 1; i > idx; --i )
{
std::uninitialized_move_n( slot( i - 1 ), 1, slot( i )
);
std::destroy_at( slot( i - 1 ) );
}
if ( idx < _count - 1 )
std::destroy_at( slot( idx ) );
std::uninitialized_move_n( &v, 1, slot( idx ) );
}
const value_t &front() const { return *slot( 0 ); }
const value_t &back() const { return *slot( _count - 1 ); }
value_t &front() { return *slot( 0 ); }
value_t &back() { return *slot( _count - 1 ); }
};
#include "test_main.cpp"
void throw_insufficient_space()
{
throw insufficient_space();
}
Part S.11: Week 11
S.11.1 [11.e1_iota]
#define UNIT e1_iota
struct iota_iterator
{
using iterator = iota_iterator;
int _val;
bool operator==( iterator o ) const { return _val == o._val; };
bool operator!=( iterator o ) const { return _val != o._val; };
iota_iterator &operator++() { ++ _val; return *this; }
int operator*() const { return _val; }
};
class iota
{
int _start, _end;
public:
iota_iterator begin() const { return { _start }; }
iota_iterator end() const { return { _end }; }
iota( int s, int e ) : _start( s ), _end( e ) {}
};
#include "test_main.cpp"
S.11.2 [11.e2_view]
#define UNIT e2_view
template< typename iter_t >
class view
{
iter_t _begin, _end;
public:
view( iter_t b, iter_t e ) : _begin( b ), _end( e ) {}
iter_t begin() const { return _begin; }
iter_t end() const { return _end; }
};
#include "test_main.cpp"
S.11.3 [11.e3_skip]
#define UNIT e3_skip
template< typename iter_t >
class skip
{
iter_t _begin, _end;
int _skip;
public:
struct iterator
{
iter_t iter, end;
int skip;
decltype( auto ) operator*() { return *iter; }
decltype( auto ) operator*() const { return *iter; }
bool operator==( iterator o ) const
{
return iter == o.iter;
}
bool operator!=( iterator o ) const
{
return iter != o.iter;
}
iterator operator++( int )
{
iterator i = *this;
++*this;
return i;
}
iterator &operator++()
{
for ( int i = 0; i < skip; ++ i )
if ( iter != end )
++iter;
return *this;
}
};
skip( iter_t b, iter_t e, int s )
: _begin( b ), _end( e ), _skip( s )
{}
iterator begin() const { return { _begin, _end, _skip }; }
iterator end() const { return { _end, _end, _skip }; }
};
#include "test_main.cpp"
S.11.4 [11.r1_map]
#define UNIT r1_map
We first define the iterator. It is convenient to take the underlying
iterator as a type parameter (instead of the container), though the
latter would also work. The other type parameter is the lambda to call
on each dereference.
template< typename iterator_t, typename fun_t >
struct map_iterator
{
iterator_t it;
const fun_t &fun;
Construct an iterator. The signature makes template argument deduction
work, which we will use to our advantage below.
map_iterator( iterator_t it, const fun_t &fun )
: it( it ), fun( fun )
{}
PB161 Programming in C++ 110/114 June 28, 2022
The dereference operator first dereferences the underlying iterator, applies
fun to it and returns the result. The return type of the dereference
operator is tricky, so we let the compiler figure it out for us.
auto operator*() const { return fun( *it ); }
Pre-increment simply calls the underlying pre-increment.
map_iterator &operator++() { ++it; return *this; }
Same thing with inequality.
bool operator!=( const map_iterator &o ) const
{
return it != o.it;
}
};
The map class template. Here we take the underlying container and the
type of the lambda as parameters, since those are what the user will
supply as arguments to the constructor. This way, template argument
deduction will work for users as expected.
template< typename container_t, typename fun_t >
struct map
{
There are two ways to go about building the iterator type. One is
explicitly, by figuring out the type of the underlying iterator (i.e. the
iterator of container_t and creating an explicit instance of map_iterator.
We will use this in begin.
using underlying = typename container_t::const_iterator;
using iterator = map_iterator< underlying, fun_t >;
const container_t &container;
const fun_t &fun;
The begin method needs to construct a suitable map_iterator: we built
the correct type above, so we can use that as the return type of begin,
then use return with braces to call the constructor.
iterator begin() const { return { container.begin(), fun }; }
An alternative, which does not need to mention the type of the underlying
iterator, but instead relies on the argument deduction that we
were careful to build into the constructor of map_iterator.
auto end() const
{
return map_iterator( container.end(), fun );
}
Finally the constructor of map which lets us conveniently create instances
through template argument deduction.
map( const container_t &c, const fun_t &f )
: container( c ), fun( f )
{}
};
#include "test_main.cpp"
S.11.5 [11.r2_range]
#define UNIT r2_range
#include <algorithm>
#include <memory>
template< typename container_t >
class range
{
using data_ptr = std::shared_ptr< container_t >;
using iterator = typename container_t::const_iterator;
data_ptr _data;
iterator _b, _e;
public:
range( container_t c )
: _data( std::make_shared< container_t >( std::move( c ) )
),
_b( _data->begin() ), _e( _data->end() )
{}
range( data_ptr c, iterator b, iterator e )
: _data( c ), _b( b ), _e( e )
{}
auto begin() const { return _b; }
auto end() const { return _e; }
range take( int n ) const
{
return { _data, _b, std::next( _b, n ) };
}
range drop( int n ) const
{
return { _data, std::next( _b, n ), _e };
}
template< typename C >
friend bool operator==( range a, range< C > b )
{
return std::equal( a.begin(), a.end(), b.begin(), b.end() );
}
};
#include "test_main.cpp"
S.11.6 [11.r3_permute]
#define UNIT r3_permute
#include <vector>
#include <algorithm>
struct permutations
{
struct permutation
{
std::vector< int > p;
auto begin() const { return p.begin(); }
auto end() const { return p.end(); }
int operator[]( int i ) const { return p[ i ]; }
};
struct iterator
{
std::vector< int > p;
iterator &operator++()
{
if ( !std::next_permutation( p.begin(), p.end() ) )
p.clear();
return *this;
}
permutation operator*() const { return { p }; }
bool operator!=( const iterator &o ) const
{
return p != o.p;
}
bool operator==( const iterator &o ) const
{
return p == o.p;
}
PB161 Programming in C++ 111/114 June 28, 2022
};
std::vector< int > first;
permutations( std::vector< int > v ) : first( std::move( v ) )
{
std::sort( first.begin(), first.end() );
}
iterator begin() const { return { first }; }
iterator end() const { return {}; }
};
#include "test_main.cpp"
S.11.7 [11.r5_matrix]
#define UNIT r5_matrix
template< typename scalar_t, size_t ncols, size_t nrows >
class matrix
{
using row = std::array< scalar_t, ncols >;
std::array< row, nrows > _data;
template< typename matrix_t, typename value_t >
struct column_iterator
{
using value_type = value_t;
using reference = value_t &;
using pointer = value_t *;
using difference_type = ssize_t;
using iterator_category = std::forward_iterator_tag;
matrix_t *_matrix;
int _col;
int _row;
column_iterator &operator++()
{
++ _row;
return *this;
}
pointer operator->() const { return &**this; }
reference operator*() const
{
return _matrix->_data[ _row ][ _col ];
}
bool operator==( column_iterator o ) const
{
return _col == o._col && _row == o._row;
}
bool operator!=( column_iterator o ) const
{
return !( *this == o );
}
};
template< typename matrix_t, typename value_t >
struct column
{
using iterator = column_iterator< matrix_t, value_t >;
matrix_t *_matrix;
int _col;
iterator begin() const { return { _matrix, _col, 0 }; }
iterator end() const { return { _matrix, _col, nrows }; }
};
template< typename value_t >
struct proxy
{
value_t _value;
value_t *operator->() { return &_value; }
};
template< typename matrix_t, typename value_t >
struct columns_iterator
{
using value_type = column< matrix_t, value_t >;
using reference = value_type;
using pointer = value_type *;
using difference_type = ssize_t;
using iterator_category = std::input_iterator_tag;
matrix_t *_matrix;
int _col;
columns_iterator &operator++()
{
++ _col;
return *this;
}
proxy< value_type > operator->() const { return { **this };
}
reference operator*() const { return { _matrix, _col }; }
bool operator==( columns_iterator o ) const
{
return o._matrix == _matrix && o._col == _col;
}
bool operator!=( columns_iterator o ) const
{
return !( *this == o );
}
};
template< typename matrix_t, typename value_t >
struct columns
{
using iterator = columns_iterator< matrix_t, value_t >;
matrix_t *_matrix;
iterator begin() const { return { _matrix, 0 }; }
iterator end() const { return { _matrix, ncols }; }
};
public:
matrix( std::initializer_list< scalar_t > il )
{
auto it = data( il );
for ( size_t i = 0; i < ncols * nrows; ++i )
{
assert( it != il.end() );
_data[ i / ncols ][ i % ncols ] = *it++;
}
assert( it == il.end() );
}
auto &rows() const { return _data; }
columns< const matrix, const scalar_t > cols() const { return {
this }; }
columns< matrix, scalar_t > cols() { return { this }; }
};
#include "test_main.cpp"
S.11.8 [11.r6_bits]
#define UNIT r6_bits
#include <iterator>
PB161 Programming in C++ 112/114 June 28, 2022
template< typename num_t >
class bits
{
struct proxy
{
bool _value;
bool *operator->() { return &_value; }
};
struct iterator
{
using value_type = bool;
using reference = bool;
using pointer = proxy;
using difference_type = ssize_t;
using iterator_category = std::input_iterator_tag;
num_t _value;
num_t _mask;
iterator &operator++()
{
_mask <<= 1;
return *this;
}
bool operator*() const { return _value & _mask; }
proxy operator->() const { return { **this }; }
bool operator==( const iterator &other ) const
{
return _mask == other._mask;
}
bool operator!=( const iterator &other ) const
{
return !( *this == other );
}
};
num_t _value;
public:
bits( num_t n ) : _value( n ) {}
iterator begin() const { return { _value, 1 }; }
iterator end() const { return { _value, 0 }; }
};
#include "test_main.cpp"
Part S.12: Week 12
S.12.1 [12.e1_digraph]
#define UNIT e1_digraph
#include <map>
#include <string>
struct strmap
{
std::map< std::string, int > m;
int operator[]( std::string s ) const
{
return m.count( s ) ? m.find( s )->second : 0;
}
void add( std::string s )
{
m[ s ] ++;
}
};
strmap digraph_freq( const std::string &s )
{
strmap m;
for ( size_t i = 0; i < s.size() - 1; ++i )
if ( std::isalpha( s[ i ] ) && std::isalpha( s[ i + 1 ] ) )
m.add( s.substr( i, 2 ) );
return m;
}
#include "test_main.cpp"
S.12.2 [12.e2_spelling]
#define UNIT e2_spelling
#include <fstream>
#include <set>
#include <string>
class spell
{
std::set< std::string > _words;
public:
spell( const char *fn )
{
std::ifstream words( fn );
std::string word;
while ( std::getline( words, word ) )
_words.insert( word );
}
bool check( const std::string s ) const
{
return _words.count( s );
}
};
#include "test_main.cpp"
S.12.3 [12.e3_ternary]
#define UNIT e3_ternary
struct tristate
{
bool val, det;
};
const tristate yes { true, true };
const tristate no { false, true };
const tristate maybe{ false, false };
tristate operator&&( tristate a, tristate b )
{
if ( a.det && b.det )
return a.val && b.val ? yes : no;
if ( ( a.det && !a.val ) || ( b.det && !b.val ) )
return no;
else
return maybe;
}
tristate operator||( tristate a, tristate b )
{
if ( a.det && b.det )
return a.val || b.val ? yes : no;
if ( ( a.det && a.val ) || ( b.det && b.val ) )
return yes;
else
return maybe;
}
PB161 Programming in C++ 113/114 June 28, 2022
bool operator==( tristate a, tristate b )
{
if ( a.det && b.det )
return a.val == b.val;
else
return a.det == b.det;
}
#include "test_main.cpp"
S.12.4 [12.r1_trie]
#define UNIT r1_trie
#include <memory>
#include <vector>
#include <cassert>
using key = std::vector< bool >;
struct node
{
std::shared_ptr< node > l, r;
std::weak_ptr< node > up;
node( std::shared_ptr< node > u )
: up( u )
{}
bool val() const
{
assert( up.lock()->l.get() == this ||
up.lock()->r.get() == this );
return up.lock()->r.get() == this;
}
::key key() const
{
::key k;
if ( up.lock() )
{
k = up.lock()->key();
k.push_back( val() );
}
return k;
}
};
class trie
{
using ptr = std::shared_ptr< node >;
ptr r;
using ref = node &;
public:
trie() : r( std::make_shared< node >( nullptr ) ) {}
auto make( ptr u ) { return std::make_shared< node >( u ); }
ptr add( ptr n, bool l )
{
return ( l ? n->r : n->l ) = make( n );
}
ptr add_amb( ptr n )
{
return n->r = n->l = make( n );
}
ptr find( key k, int idx, ptr n ) const
{
if ( idx == int( k.size() ) ) return n;
return find( k, idx + 1, k[ idx ] ? n->r : n->l );
}
ptr find( key k ) const { return find( k, 0, r ); }
ptr root() const { return r; }
};
#include "test_main.cpp"
S.12.5 [12.r2_cooking]
#define UNIT r2_cooking
#include <map>
#include <string>
class pantry
{
public:
std::map< std::string, int > stuff;
int count( std::string s ) const { return stuff.at( s ); }
void add( std::string s, int v ) { stuff[ s ] += v; }
};
class recipe
{
public:
std::map< std::string, std::pair< int, int > > stuff;
void add( std::string s, int v, int o = 0 )
{
stuff[ s ].first += v;
stuff[ s ].second += o;
}
};
bool cook( pantry &p, const recipe &r, int qty )
{
for ( const auto &[ k, v ] : r.stuff )
if ( qty * v.first > p.count( k ) )
return false;
for ( const auto &[ k, v ] : r.stuff )
{
p.stuff[ k ] -= qty * v.first;
if ( p.count( k ) > qty * v.second )
p.stuff[ k ] -= qty * v.second;
}
return true;
}
#include "test_main.cpp"
S.12.6 [12.r3_cards]
#define UNIT r3_cards
#include <sstream>
class card
{
char suit, rank;
public:
friend std::ostream &operator<<( std::ostream &o, card c )
{
return o << c.rank << c.suit;
}
friend std::istream &operator>>( std::istream &i, card &c )
{
char ch;
i >> ch;
if ( ( !std::isdigit( ch ) &&
ch != 'A' && ch != 'J' && ch != 'Q' &&
ch != 'K' && ch != 'T' ) ||
( i.peek() != 'D' && i.peek() != 'S' &&
i.peek() != 'H' && i.peek() != 'C' ) ||
PB161 Programming in C++ 114/114 June 28, 2022
ch == '0' )
{
i.unget();
i.setstate( i.failbit );
return i;
}
c.rank = ch;
return i >> c.suit;
}
};
#include "test_main.cpp"